Mean Value Theorems and Functional Equations

Mean Value Theorems and Functional Equations
Title Mean Value Theorems and Functional Equations PDF eBook
Author Prasanna Sahoo
Publisher World Scientific
Pages 268
Release 1998
Genre Mathematics
ISBN 9789810235444

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This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.

Functional Equations, Inequalities and Applications

Functional Equations, Inequalities and Applications
Title Functional Equations, Inequalities and Applications PDF eBook
Author Themistocles M. Rassias
Publisher Springer Science & Business Media
Pages 244
Release 2003-09-30
Genre Mathematics
ISBN 9781402015786

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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.

Introduction to Functional Equations

Introduction to Functional Equations
Title Introduction to Functional Equations PDF eBook
Author Prasanna K. Sahoo
Publisher CRC Press
Pages 459
Release 2011-02-08
Genre Mathematics
ISBN 1439841160

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Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as p

Stability of Functional Equations in Random Normed Spaces

Stability of Functional Equations in Random Normed Spaces
Title Stability of Functional Equations in Random Normed Spaces PDF eBook
Author Yeol Je Cho
Publisher Springer Science & Business Media
Pages 255
Release 2013-08-27
Genre Mathematics
ISBN 1461484774

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This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.

Functional Equations, Inequalities and Applications

Functional Equations, Inequalities and Applications
Title Functional Equations, Inequalities and Applications PDF eBook
Author Themistocles RASSIAS
Publisher Springer Science & Business Media
Pages 221
Release 2013-03-09
Genre Mathematics
ISBN 940170225X

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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.

Implicit Functions and Solution Mappings

Implicit Functions and Solution Mappings
Title Implicit Functions and Solution Mappings PDF eBook
Author Asen L. Dontchev
Publisher Springer
Pages 495
Release 2014-06-18
Genre Mathematics
ISBN 149391037X

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The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Functional Equations and Inequalities with Applications

Functional Equations and Inequalities with Applications
Title Functional Equations and Inequalities with Applications PDF eBook
Author Palaniappan Kannappan
Publisher Springer Science & Business Media
Pages 817
Release 2009-06-10
Genre Mathematics
ISBN 0387894926

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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.