George Anastassiou's Books

Intelligent Comparisons: Analytic Inequalities

By: George A. Anastassiou

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Intelligent Comparisons: Analytic Inequalities

By: George A. Anastassiou

This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter. The book’s results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.

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663

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Springer

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ISBN 10

3319211218

ISBN 13

9783319211213

Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

By: George A. Anastassiou

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Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

By: George A. Anastassiou

This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.

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322

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Springer

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ISBN 10

3319669362

ISBN 13

9783319669366

Intelligent Comparisons II: Operator Inequalities and Approximations

By: George A. Anastassiou

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Intelligent Comparisons II: Operator Inequalities and Approximations

By: George A. Anastassiou

This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

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231

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Springer

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ISBN 10

331951475X

ISBN 13

9783319514758

Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

This book presents applications of Newton-like and other similar methods to solve abstract functional equations involving fractional derivatives. It focuses on Banach space-valued functions of a real domain – studied for the first time in the literature. Various issues related to the modeling and analysis of fractional order systems continue to grow in popularity, and the book provides a deeper and more formal analysis of selected issues that are relevant to many areas – including decision-making, complex processes, systems modeling and control – and deeply embedded in the fields of engineering, computer science, physics, economics, and the social and life sciences. The book offers a valuable resource for researchers and graduate students, and can also be used as a textbook for seminars on the above-mentioned subjects. All chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references.

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166

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Springer

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ISBN 10

3319695266

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9783319695266

Abstract Fractional Monotone Approximation, Theory and Applications

By: George A. Anastassiou

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Abstract Fractional Monotone Approximation, Theory and Applications

By: George A. Anastassiou

This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.

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155

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Springer Nature

Published Date

ISBN 10

3030959430

ISBN 13

9783030959432

Numerical Analysis Using Sage

By: George A. Anastassiou,Razvan A. Mezei

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Numerical Analysis Using Sage

By: George A. Anastassiou,Razvan A. Mezei

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage. The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink.com.

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321

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Springer

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ISBN 10

3319167391

ISBN 13

9783319167398

Ophthalmic Surgery: Principles and Practice E-Book

By: George L. Spaeth,Helen Danesh-Meyer,Ivan Goldberg,Anselm Kampik

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Ophthalmic Surgery: Principles and Practice E-Book

By: George L. Spaeth,Helen Danesh-Meyer,Ivan Goldberg,Anselm Kampik

Ophthalmic Surgery, edited by Drs. George Spaeth, Helen Danesh-Meyer, Ivan Goldberg, and Anselm Kampik, provides the detailed, full-color, step-by-step guidance you need to master essential ophthalmic surgery procedures. The international team of expert editors and contributors present coverage of the latest surgical developments and video demonstrations of key techniques across subspecialties, including cataract, cornea, refractive, glaucoma, oculoplastic, extra-ocular muscle, vitreoretinal, and ocular tumor procedures. What’s more, the fully searchable text, procedural videos, and a downloadable image gallery are all online at www.expertconsult.com, making this multimedia resource the key to performing confidently in the operating room. Refer to the most important steps in each procedure quickly and easily with an appendix of step-by-step hand notes. Perform a wide variety of procedures with confidence using the focused coverage that pinpoints essential information and avoids extraneous details. Get comprehensive coverage across key subspecialties—oculoplastic, strabismus, cornea, refractive, cataract, glaucoma, ocular tumors, and vitreoretinal—and master the basics for every common procedure. Access the fully searchable contents online at www.expertconsult.com, along with procedural videos and a downloadable image gallery. Apply the latest advances in laser surgery that have become standard practice with the new section on refractive surgery. Master key techniques thanks to more than four hours of narrated online videos that demonstrate procedures across eight subspecialties. Gain a more nuanced visual understanding through a new full-color art program with over 800 illustrations, updated and revised drawings, color images, and step-by-step illustrated procedures. Tap into the expertise of leading authorities in the field with a brand new editorial team from North America, Europe, and Australasia, as well as international contributors who provide global perspectives across all subspecialties in ophthalmic surgery.

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673

Publisher

Elsevier Health Sciences

Published Date

ISBN 10

1455712337

ISBN 13

9781455712335

Delta-sigma Modulators: Modeling, Design And Applications

By: Vassilis Anastassopoulos,George Bourdopoulos,Theodore L Deliyannis,Aristodemos Pnevmatikakis

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Delta-sigma Modulators: Modeling, Design And Applications

By: Vassilis Anastassopoulos,George Bourdopoulos,Theodore L Deliyannis,Aristodemos Pnevmatikakis

This important book deals with the modeling and design of higher-order single-stage delta-sigma modulators. It provides an overview of the architectures, the quantizer models, the design techniques and the implementation issues encountered in the study of the delta-sigma modulators. A number of applications are discussed, with emphasis on use in the design of analog-to-digital converters and in frequency synthesis. The book is education- rather than research-oriented, containing numerical examples and unsolved problems. It is aimed at introducing the final-year undergraduate, the graduate student or the electronic engineer to this field.

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259

Publisher

World Scientific

Published Date

ISBN 10

1783260920

ISBN 13

9781783260928

Platonist Philosophy 80 BC to AD 250

An Introduction and Collection of Sources in Translation

By: George Boys-Stones

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Platonist Philosophy 80 BC to AD 250

An Introduction and Collection of Sources in Translation

By: George Boys-Stones

Middle' Platonism has some claim to be the single most influential philosophical movement of the last two thousand years, as the common background to 'Neoplatonism' and the early development of Christian theology. This book breaks with the tradition of considering it primarily in terms of its sources, instead putting its contemporary philosophical engagements front and centre to reconstruct its philosophical motivations and activity across the full range of its interests. The volume explores the ideas at the heart of Platonist philosophy in this period and includes a comprehensive selection of primary sources, a significant number of which appear in English translation for the first time, along with dedicated guides to the questions that have been, and might be, asked about the movement. The result is a tool intended to help bring the study of Middle Platonism into mainstream discussions of ancient philosophy.

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1047

Publisher

Cambridge University Press

Published Date

ISBN 10

1108228097

ISBN 13

9781108228091

Supply Chain and Finance

By: Panos M. Pardalos,Athanasios Migdalas,George Baourakis

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Supply Chain and Finance

By: Panos M. Pardalos,Athanasios Migdalas,George Baourakis

This book describes recently developed mathematical models, methodologies, and case studies in diverse areas, including stock market analysis, portfolio optimization, classification techniques in economics, supply chain optimization, development of e-commerce applications, etc. It will be of interest to both theoreticians and practitioners working in economics and finance.

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359

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World Scientific

Published Date

ISBN 10

981238717X

ISBN 13

9789812387172

Electroencephalography and Magnetoencephalography

An Analytical-Numerical Approach

By: George Dassios,Athanassios S. Fokas

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Electroencephalography and Magnetoencephalography

An Analytical-Numerical Approach

By: George Dassios,Athanassios S. Fokas

Electroencephalography and magnetoencephalography are the two most efficient techniques to study the functional brain. This book completely aswers the fundamental mathematical question of uniqueness of the representations obtained using these techniques, and also covers many other concrete results for special geometric models of the brain, presenting the research of the authors and their groups in the last two decades.

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192

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110545780

ISBN 13

9783110545784

Expert Techniques in Ophthalmic Surgery

By: Parul Ichhpujani,George L Spaeth,Myron Yanoff

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Expert Techniques in Ophthalmic Surgery

By: Parul Ichhpujani,George L Spaeth,Myron Yanoff

The second edition of this comprehensive, 1032-pages text and atlas provides ophthalmic surgeons and trainees with the latest advances and techniques in their field. Divided into ten sections, the book begins with an overview of the basic principles of ophthalmic surgery. Each of the following sections is dedicated to surgical procedures for diseases and disorders in different parts of the eye. Surgical techniques are explained in a step by step format and each section is colour-coded for easy cross reference and navigation. Ethics and medico-legal issues are also discussed in depth. Authored by internationally recognised experts in ophthalmic surgery, this new edition has been fully revised and updated. Nearly 1000 clinical photographs, illustrations and tables further enhance the extensive text. Key points Comprehensive text and atlas providing latest advances and techniques in ophthalmic surgery Fully revised, second edition with nearly 1000 photographs, illustrations and tables Internationally recognised author team Previous edition (9789351525004) published in 2015

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1032

Publisher

Jaypee Brothers Medical Publishers

Published Date

ISBN 10

9352709748

ISBN 13

9789352709748

Boundary-field Equation Methods For a Class of Nonlinear Problems

By: Gabriel N Gatica,George C Hsiao

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Boundary-field Equation Methods For a Class of Nonlinear Problems

By: Gabriel N Gatica,George C Hsiao

This book is the first to offer a general discussion on the cupling methods for nonliner problems, and provides all material necessary for an introductory course on the subject. Readers are assumed to have only a basic knowledge of applied functional analysis and partial differential equations at graduate level. This book can be used as an advanced graduate text as well as a reference for specialists working in the areas of partial differential equations, boundary integral equations and scientific computing. This book will be of particular interest to students and researchers in applied mathematics, numerical analysis and partial differential equations.

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196

Publisher

CRC Press

Published Date

ISBN 10

0582279690

ISBN 13

9780582279698

Quantitative Approximations

By: George Anastassiou

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Quantitative Approximations

By: George Anastassiou

Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.

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626

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CRC Press

Published Date

ISBN 10

1584882212

ISBN 13

9781584882213

Mathematical Methods in Scattering Theory and Biomedical Technology

By: George Dassios,Dimitrios I Fotiadis,Christos V Massalas,Kiriakie Kiriaki

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Mathematical Methods in Scattering Theory and Biomedical Technology

By: George Dassios,Dimitrios I Fotiadis,Christos V Massalas,Kiriakie Kiriaki

The papers in this volume address the state-of-the-art and future directions in applied mathematics in both scattering theory and biomedical technology. A workshop held in Metsovo, Greece during the summer of 1997 brought together some of the world's foremose experts in the field with researchers working in Greece. Sixteen of the contributed papers appear in this volume. All the papers give new directions, and in several cases, the most important scientific contributions in the fields.

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252

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CRC Press

Published Date

ISBN 10

0582368049

ISBN 13

9780582368040

Fractional Differentiation Inequalities

By: George A. Anastassiou

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Fractional Differentiation Inequalities

By: George A. Anastassiou

In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful.

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672

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387981284

ISBN 13

9780387981284

Parametrized, Deformed and General Neural Networks

By: George A. Anastassiou

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Parametrized, Deformed and General Neural Networks

By: George A. Anastassiou

In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

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854

Publisher

Springer Nature

Published Date

ISBN 10

3031430212

ISBN 13

9783031430213

Fractional Differentiation Inequalities

By: George A. Anastassiou

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Fractional Differentiation Inequalities

By: George A. Anastassiou

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672

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Springer Science & Business Media

Published Date

ISBN 10

0387981284

ISBN 13

9780387981284

Advanced Inequalities

By: George A Anastassiou

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Advanced Inequalities

By: George A Anastassiou

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, Gruss and Comparison of Means inequalities are studied.The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

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423

Publisher

World Scientific

Published Date

ISBN 10

9814464341

ISBN 13

9789814464345

Approximation Theory

Moduli of Continuity and Global Smoothness Preservation

By: George A. Anastassiou,Sorin G. Gal

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Approximation Theory

Moduli of Continuity and Global Smoothness Preservation

By: George A. Anastassiou,Sorin G. Gal

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

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520

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Springer Science & Business Media

Published Date

ISBN 10

1461213606

ISBN 13

9781461213604

Frontiers in Time Scales and Inequalities

By: George A. Anastassiou

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Frontiers in Time Scales and Inequalities

By: George A. Anastassiou

This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.

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278

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9814704431

ISBN 13

9789814704434

Constructive Fractional Analysis with Applications

By: George A. Anastassiou

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Constructive Fractional Analysis with Applications

By: George A. Anastassiou

This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss–Weierstrass, Poisson–Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann–Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert–Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.

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523

Publisher

Springer Nature

Published Date

ISBN 10

3030714810

ISBN 13

9783030714819

Numerical Analysis Using Sage

By: George A. Anastassiou,Razvan A. Mezei

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Numerical Analysis Using Sage

By: George A. Anastassiou,Razvan A. Mezei

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321

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Springer

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ISBN 10

3319167391

ISBN 13

9783319167398

Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

By: George A. Anastassiou

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Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

By: George A. Anastassiou

Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

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355

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Springer

Published Date

ISBN 10

3030042871

ISBN 13

9783030042875

Intelligent Systems: Approximation by Artificial Neural Networks

By: George A. Anastassiou

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Intelligent Systems: Approximation by Artificial Neural Networks

By: George A. Anastassiou

This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author's last two years of related research work. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science libraries.

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113

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Springer Science & Business Media

Published Date

ISBN 10

3642214312

ISBN 13

9783642214318

Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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166

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Springer

Published Date

ISBN 10

3319695266

ISBN 13

9783319695266

Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators

By: George A. Anastassiou

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Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators

By: George A. Anastassiou

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory –approximation by sublinear operators with applications to max-product operators, which are nonlinear and rational providing very fast and flexible approximations. The results presented have applications in numerous areas of pure and applied mathematics, especially in approximation theory and numerical analysis in both ordinary and fractional senses. As such this book is suitable for researchers, graduate students, and seminars of the above disciplines, and is a must for all science and engineering libraries.

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298

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Springer

Published Date

ISBN 10

3319895095

ISBN 13

9783319895093

Towards Intelligent Modeling: Statistical Approximation Theory

By: George A. Anastassiou,Oktay Duman

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Towards Intelligent Modeling: Statistical Approximation Theory

By: George A. Anastassiou,Oktay Duman

The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.

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Page Count

239

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642198260

ISBN 13

9783642198267

Generalized Fractional Calculus

New Advancements and Applications

By: George A. Anastassiou

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Generalized Fractional Calculus

New Advancements and Applications

By: George A. Anastassiou

This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.

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501

Publisher

Springer Nature

Published Date

ISBN 10

3030569624

ISBN 13

9783030569624

Frontiers In Approximation Theory

By: George A Anastassiou

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Frontiers In Approximation Theory

By: George A Anastassiou

This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.

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229

Publisher

World Scientific

Published Date

ISBN 10

9814696110

ISBN 13

9789814696111

Inequalities Based on Sobolev Representations

By: George A. Anastassiou

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Inequalities Based on Sobolev Representations

By: George A. Anastassiou

Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Grüss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory.

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Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461402018

ISBN 13

9781461402015

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