Th M Rassias's Books

On Extended Hardy-hilbert Integral Inequalities And Applications

By: Bicheng Yang,Michael Th Rassias

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On Extended Hardy-hilbert Integral Inequalities And Applications

By: Bicheng Yang,Michael Th Rassias

Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities.In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators.Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.

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Page Count

203

Publisher

World Scientific

Published Date

ISBN 10

9811267111

ISBN 13

9789811267116

Problem-Solving and Selected Topics in Euclidean Geometry

In the Spirit of the Mathematical Olympiads

By: Sotirios E. Louridas,Michael Th. Rassias

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Problem-Solving and Selected Topics in Euclidean Geometry

In the Spirit of the Mathematical Olympiads

By: Sotirios E. Louridas,Michael Th. Rassias

Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.

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238

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Springer Science & Business Media

Published Date

ISBN 10

1461472733

ISBN 13

9781461472735

Goldbach’s Problem

Selected Topics

By: Michael Th. Rassias

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Goldbach’s Problem

Selected Topics

By: Michael Th. Rassias

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem. The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.

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129

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Springer

Published Date

ISBN 10

3319579142

ISBN 13

9783319579146

Problem-Solving and Selected Topics in Number Theory

In the Spirit of the Mathematical Olympiads

By: Michael Th. Rassias

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Problem-Solving and Selected Topics in Number Theory

In the Spirit of the Mathematical Olympiads

By: Michael Th. Rassias

The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

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Page Count

336

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Springer Science & Business Media

Published Date

ISBN 10

1441904948

ISBN 13

9781441904942

Moments of Linear Positive Operators and Approximation

By: Vijay Gupta,Michael Th. Rassias

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Moments of Linear Positive Operators and Approximation

By: Vijay Gupta,Michael Th. Rassias

This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.

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102

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Springer

Published Date

ISBN 10

3030194558

ISBN 13

9783030194550

Computation and Approximation

By: Vijay Gupta,Michael Th. Rassias

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Computation and Approximation

By: Vijay Gupta,Michael Th. Rassias

This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.

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Page Count

107

Publisher

Springer Nature

Published Date

ISBN 10

3030855635

ISBN 13

9783030855635

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

By: Bicheng Yang,Michael Th. Rassias

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On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

By: Bicheng Yang,Michael Th. Rassias

This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of real analysis and functional analysis are applied to equivalent formulations of Hilbert-type inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special cases of these integral inequalities across an entire plane are considered and explained. Operator expressions with the norm and some particular analytic inequalities are detailed through several lemmas and theorems to provide an extensive account of inequalities and operators.

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152

Publisher

Springer Nature

Published Date

ISBN 10

3030292681

ISBN 13

9783030292683

Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

By: Helmut Maier,Michael Th Rassias,Laszlo Toth

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Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

By: Helmut Maier,Michael Th Rassias,Laszlo Toth

In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums — which constitute a very classical domain of research in Number Theory — as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretèche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.

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Page Count

165

Publisher

World Scientific

Published Date

ISBN 10

9811246904

ISBN 13

9789811246906

Exploring Mathematical Analysis, Approximation Theory, and Optimization

270 Years Since A.-M. Legendre’s Birth

By: Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos

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Exploring Mathematical Analysis, Approximation Theory, and Optimization

270 Years Since A.-M. Legendre’s Birth

By: Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

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Page Count

474

Publisher

Springer Nature

Published Date

ISBN 10

3031464877

ISBN 13

9783031464874

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

By: Bicheng Yang,Michael Th. Rassias

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On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

By: Bicheng Yang,Michael Th. Rassias

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152

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Springer Nature

Published Date

ISBN 10

3030292681

ISBN 13

9783030292683

Moments of Linear Positive Operators and Approximation

By: Vijay Gupta,Michael Th. Rassias

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Moments of Linear Positive Operators and Approximation

By: Vijay Gupta,Michael Th. Rassias

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102

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Springer

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3030194558

ISBN 13

9783030194550

Book's by Th M Rassias

On Extended Hardy-hilbert Integral Inequalities And Applications

On Extended Hardy-hilbert Integral Inequalities And Applications

Problem-Solving and Selected Topics in Euclidean Geometry

Problem-Solving and Selected Topics in Euclidean Geometry

Goldbach’s Problem

Goldbach’s Problem

Problem-Solving and Selected Topics in Number Theory

Problem-Solving and Selected Topics in Number Theory

Moments of Linear Positive Operators and Approximation

Moments of Linear Positive Operators and Approximation

Computation and Approximation

Computation and Approximation

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

Exploring Mathematical Analysis, Approximation Theory, and Optimization

Exploring Mathematical Analysis, Approximation Theory, and Optimization

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

Moments of Linear Positive Operators and Approximation

Moments of Linear Positive Operators and Approximation

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