Functional Equations And Inequalities With Applications

Author : Palaniappan Kannappan
Publisher : Springer Science & Business Media
Page : 817 pages
File Size : 51,9 Mb
Release : 2009-06-10
Category : Mathematics
ISBN : 9780387894928

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Functional Equations and Inequalities with Applications by Palaniappan Kannappan Pdf

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.

Author : Themistocles RASSIAS
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 48,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401702256

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Functional Equations, Inequalities and Applications by Themistocles RASSIAS Pdf

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

Author : B. Forte
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 44,6 Mb
Release : 2011-06-02
Category : Mathematics
ISBN : 9783642110047

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Functional Equations and Inequalities by B. Forte Pdf

J. Aczél: Some applications of functional equations and inequalities to information measures.- J.A. Baker: Functional equations in vector space, part II.- I Fenyo: Sur les équations distributionnelles.- B. Forte: Applications of functional equations and inequalities to information theory.- S. Golab: Sur l’équation fonctionnelle des brigade.- E. Hille: Mean-values and functional equations.- J. Kampé de Feriet: Applications of functional equations and inequalities to information theory. Measure of information by a set of observers: a functional equation.- M. Kuczma: Convex functions.- S. Kurepa: Functional equations on vector spaces.- E. Lukacs: Inequalities and functional equations in probability theory.- M.A. McKiernan: Difference and mean-value type functional equations.- T.S. Motzkin: Solutions of differential and functional inequalities.- C.T. Ng: Uniqueness theorems in the theory of functional equations and related homotopy.- A.M. Ostrowski: Integral inequalities.- H. Schwerdtfeger: Remark on an inequality for monotonic functions.

Author : Themistocles M. Rassias
Publisher : Springer
Page : 555 pages
File Size : 42,9 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781493912469

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Handbook of Functional Equations by Themistocles M. Rassias Pdf

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Author : Stefan Czerwik
Publisher : World Scientific
Page : 424 pages
File Size : 47,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9810248377

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Functional Equations and Inequalities in Several Variables by Stefan Czerwik Pdf

This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with ? for the first time in the mathematical literature. The book contains many fresh results concerning those problems.

Author : Themistocles RASSIAS
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401143417

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Functional Equations and Inequalities by Themistocles RASSIAS Pdf

This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition of trigonometric functions, the functional equation of the square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution of zeros and inequalities for zeros of algebraic polynomials, a qualitative study of Lobachevsky's complex functional equation, functional inequalities in special classes of functions, replicativity and function spaces, normal distributions, some difference equations, finite sums, decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problems of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszú's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, integral transforms, and operational calculus.

Author : John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar
Publisher : World Scientific Publishing Company
Page : 396 pages
File Size : 41,5 Mb
Release : 2017-03-20
Category : Electronic
ISBN : 9789813147621

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Functional Equations and Inequalities by John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar Pdf

This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations. Request Inspection Copy

Author : George A. Anastassiou,John Michael Rassias
Publisher : Springer Nature
Page : 746 pages
File Size : 45,6 Mb
Release : 2019-11-23
Category : Mathematics
ISBN : 9783030289508

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Frontiers in Functional Equations and Analytic Inequalities by George A. Anastassiou,John Michael Rassias Pdf

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Author : Marek Kuczma
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 50,8 Mb
Release : 2009-03-12
Category : Mathematics
ISBN : 9783764387495

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An Introduction to the Theory of Functional Equations and Inequalities by Marek Kuczma Pdf

Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)

Author : Themistocles M. Rassias
Publisher : Springer
Page : 336 pages
File Size : 48,7 Mb
Release : 2011-09-28
Category : Mathematics
ISBN : 9401143420

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Functional Equations and Inequalities by Themistocles M. Rassias Pdf

Author : Themistocles M. Rassias
Publisher : Springer
Page : 396 pages
File Size : 42,9 Mb
Release : 2014-11-21
Category : Mathematics
ISBN : 9781493912865

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Handbook of Functional Equations by Themistocles M. Rassias Pdf

This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.

Author : Janusz Brzdęk,Krzysztof Ciepliński,Themistocles M. Rassias
Publisher : Springer
Page : 354 pages
File Size : 45,5 Mb
Release : 2017-08-14
Category : Mathematics
ISBN : 9783319617329

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Developments in Functional Equations and Related Topics by Janusz Brzdęk,Krzysztof Ciepliński,Themistocles M. Rassias Pdf

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Author : Themistocles M. Rassias,Janusz Brzdek
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 46,9 Mb
Release : 2011-09-18
Category : Mathematics
ISBN : 9781461400554

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Functional Equations in Mathematical Analysis by Themistocles M. Rassias,Janusz Brzdek Pdf

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.

Author : R.P. Agarwal,P.Y. Pang
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 41,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584265

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Opial Inequalities with Applications in Differential and Difference Equations by R.P. Agarwal,P.Y. Pang Pdf

In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.

Author : J. Aczel,Hansjorg Oser
Publisher : Courier Corporation
Page : 548 pages
File Size : 47,9 Mb
Release : 2006-02-01
Category : Mathematics
ISBN : 9780486445236

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Lectures on Functional Equations and Their Applications by J. Aczel,Hansjorg Oser Pdf

Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.