Approximation Theory And Analytic Inequalities

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Approximation Theory and Analytic Inequalities

Themistocles M. Rassias
Approximation Theory and Analytic Inequalities Book PDF

Author : Themistocles M. Rassias
Publisher : Springer Nature
Page : 546 pages
File Size : 53,8 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9783030606220

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Approximation Theory and Analytic Inequalities by Themistocles M. Rassias Pdf

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Approximation Theory and Analytic Inequalities

Themistocles M. Rassias
Approximation Theory and Analytic Inequalities Book PDF

Author : Themistocles M. Rassias
Publisher : Unknown
Page : 0 pages
File Size : 46,9 Mb
Release : 2021
Category : Electronic
ISBN : 3030606236

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Approximation Theory and Analytic Inequalities by Themistocles M. Rassias Pdf

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss-Jacobi and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam's stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Analytic Number Theory, Approximation Theory, and Special Functions

Gradimir V. Milovanović,Michael Th. Rassias
Analytic Number Theory Approximation Theory and Special Functions Book PDF

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 880 pages
File Size : 47,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Differential and Integral Inequalities

Dorin Andrica,Themistocles M. Rassias
Differential and Integral Inequalities Book PDF

Author : Dorin Andrica,Themistocles M. Rassias
Publisher : Springer Nature
Page : 848 pages
File Size : 49,7 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9783030274078

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Differential and Integral Inequalities by Dorin Andrica,Themistocles M. Rassias Pdf

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Analytic Inequalities

Dragoslav S. Mitrinovic
Analytic Inequalities Book PDF

Author : Dragoslav S. Mitrinovic
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642999703

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Analytic Inequalities by Dragoslav S. Mitrinovic Pdf

The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the continuing and growing interest in this field, undoubtedly stem from this work. The second English edition of this book, published in 1952, was unchanged except for three appendices, totalling 10 pages, added at the end of the book. Today inequalities playa significant role in all fields of mathematics, and they present a very active and attractive field of research. J. DIEUDONNE, in his book "Calcullnfinitesimal" (Paris 1968), attri buted special significance to inequalities, adopting the method of exposi tion characterized by "majorer, minorer, approcher". Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.

Nonlinear Analysis

Panos M. Pardalos,Pando G. Georgiev,Hari M. Srivastava
Nonlinear Analysis Book PDF

Author : Panos M. Pardalos,Pando G. Georgiev,Hari M. Srivastava
Publisher : Springer Science & Business Media
Page : 898 pages
File Size : 52,9 Mb
Release : 2012-06-02
Category : Mathematics
ISBN : 9781461434986

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Nonlinear Analysis by Panos M. Pardalos,Pando G. Georgiev,Hari M. Srivastava Pdf

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Analytic Inequalities

Nicholas D. Kazarinoff
Analytic Inequalities Book PDF

Author : Nicholas D. Kazarinoff
Publisher : Courier Corporation
Page : 99 pages
File Size : 46,7 Mb
Release : 2014-10-15
Category : Mathematics
ISBN : 9780486432441

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Analytic Inequalities by Nicholas D. Kazarinoff Pdf

Mathematical analysis is largely a systematic study and exploration of inequalities — but for students the study of inequalities often remains a foreign country, difficult of access. This book is a passport to that country, offering a background on inequalities that will prepare undergraduates (and even high school students) to cope with the concepts of continuity, derivative, and integral. Beginning with explanations of the algebra of inequalities and conditional inequalities, the text introduces a pair of ancient theorems and their applications. Explorations of inequalities and calculus cover the number e, examples from the calculus, and approximations by polynomials. The final sections present modern theorems, including Bernstein's proof of the Weierstrass approximation theorem and the Cauchy, Bunyakovskii, Hölder, and Minkowski inequalities. Numerous figures, problems, and examples appear throughout the book, offering students an excellent foundation for further studies of calculus.

Operators, Inequalities and Approximation

Binod Chandra Tripathy,Hemen Dutta,Susanta Kumar Paikray,Bidu Bhusan Jena
Operators Inequalities and Approximation Book PDF

Author : Binod Chandra Tripathy,Hemen Dutta,Susanta Kumar Paikray,Bidu Bhusan Jena
Publisher : Springer
Page : 0 pages
File Size : 46,7 Mb
Release : 2024-08-11
Category : Mathematics
ISBN : 9819732379

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Operators, Inequalities and Approximation by Binod Chandra Tripathy,Hemen Dutta,Susanta Kumar Paikray,Bidu Bhusan Jena Pdf

The book collects chapters on operator theory as well as related approximation results and analytic inequalities. It discusses the properties of various types of operators, methods for approximating such operators, proximity point problems, applications of approximation methods in other fields such as engineering, and some analytic inequalities. It seeks to capture both the pure and applied aspects of the topics discussed. Several of the concepts covered in the book are fundamental to many aspects of applied science and engineering. The intriguing and novel aspect of the book is that it focuses on foundational aspects of the topics as well as reasonable application ideas and inputs useful information for practical applications in a variety of other scientific and engineering fields.

New Trends in Approximation Theory

Javad Mashreghi,Myrto Manolaki,Paul Gauthier
New Trends in Approximation Theory Book PDF

Author : Javad Mashreghi,Myrto Manolaki,Paul Gauthier
Publisher : Springer
Page : 278 pages
File Size : 45,6 Mb
Release : 2018-03-28
Category : Mathematics
ISBN : 9781493975433

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New Trends in Approximation Theory by Javad Mashreghi,Myrto Manolaki,Paul Gauthier Pdf

The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

Mathematical Analysis, Approximation Theory and Their Applications

Themistocles M. Rassias,Vijay Gupta
Mathematical Analysis Approximation Theory and Their Applications Book PDF

Author : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Page : 741 pages
File Size : 46,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9783319312811

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Mathematical Analysis, Approximation Theory and Their Applications by Themistocles M. Rassias,Vijay Gupta Pdf

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Progress in Approximation Theory and Applicable Complex Analysis

Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser
Progress in Approximation Theory and Applicable Complex Analysis Book PDF

Author : Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser
Publisher : Springer
Page : 519 pages
File Size : 53,6 Mb
Release : 2017-04-03
Category : Mathematics
ISBN : 9783319492421

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Progress in Approximation Theory and Applicable Complex Analysis by Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser Pdf

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Analytic Inequalities

B.G. Pachpatte
Analytic Inequalities Book PDF

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 41,5 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9789491216442

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Analytic Inequalities by B.G. Pachpatte Pdf

For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Exploring Mathematical Analysis, Approximation Theory, and Optimization

Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Exploring Mathematical Analysis Approximation Theory and Optimization Book PDF

Author : Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Publisher : Springer Nature
Page : 474 pages
File Size : 40,8 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031464874

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Exploring Mathematical Analysis, Approximation Theory, and Optimization by Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos Pdf

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.

Classical and New Inequalities in Analysis

Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
Classical and New Inequalities in Analysis Book PDF

Author : Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
Publisher : Springer Science & Business Media
Page : 739 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401710435

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Classical and New Inequalities in Analysis by Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink Pdf

This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.

Approximation Theory and Harmonic Analysis on Spheres and Balls

Feng Dai,Yuan Xu
Approximation Theory and Harmonic Analysis on Spheres and Balls Book PDF

Author : Feng Dai,Yuan Xu
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 49,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461466604

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Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai,Yuan Xu Pdf

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.