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Hyers Ulam Rassias Stability of Functional Equations in Nonlinear Analysis

Hyers Ulam Rassias Stability of Functional Equations in Nonlinear Analysis Author Soon-Mo Jung
ISBN-10 1441996370
Release 2011-04-11
Pages 362
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No books dealing with a comprehensive illustration of the fast developing field of nonlinear analysis had been published for the mathematicians interested in this field for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias published their book, "Stability of Functional Equations in Several Variables". This book will complement the books of Hyers, Isac and Rassias and of Czerwik (Functional Equations and Inequalities in Several Variables) by presenting mainly the results applying to the Hyers-Ulam-Rassias stability. Many mathematicians have extensively investigated the subjects on the Hyers-Ulam-Rassias stability. This book covers and offers almost all classical results on the Hyers-Ulam-Rassias stability in an integrated and self-contained fashion.

Handbook of Functional Equations

Handbook of Functional Equations Author Themistocles M. Rassias
ISBN-10 9781493912865
Release 2014-11-21
Pages 396
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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.

Developments in Functional Equations and Related Topics

Developments in Functional Equations and Related Topics Author
ISBN-10 9783319617329
Release 2017
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Developments in Functional Equations and Related Topics has been writing in one form or another for most of life. You can find so many inspiration from Developments in Functional Equations and Related Topics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Developments in Functional Equations and Related Topics book for free.

Ulam Stability of Operators

Ulam Stability of Operators Author Janusz Brzdek
ISBN-10 9780128098301
Release 2018-01-10
Pages 236
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Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations. Allows readers to establish expert knowledge without extensive study of other books Presents complex math in simple and clear language Compares, generalizes and complements key findings Provides numerous open problems

Nonlinear Analysis and Variational Problems

Nonlinear Analysis and Variational Problems Author Panos M. Pardalos
ISBN-10 9781441901583
Release 2009-10-20
Pages 490
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The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Functional Equations in Mathematical Analysis

Functional Equations in Mathematical Analysis Author Themistocles M. Rassias
ISBN-10 9781461400554
Release 2011-09-18
Pages 748
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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.

Stability of Functional Equations in Several Variables

Stability of Functional Equations in Several Variables Author D.H. Hyers
ISBN-10 9781461217909
Release 2012-12-06
Pages 318
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The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co author and friend Professor Donald H. Hyers passed away.

Functional Equations and Inequalities with Applications

Functional Equations and Inequalities with Applications Author Palaniappan Kannappan
ISBN-10 9780387894928
Release 2009-06-10
Pages 810
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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.

Stability of Functional Equations in Banach Algebras

Stability of Functional Equations in Banach Algebras Author Yeol Je Cho
ISBN-10 9783319187082
Release 2015-06-26
Pages 343
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Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the latest results in mathematical analysis. Moreover, research mathematicians, physicists and engineers will benefit from the variety of old and new results, as well as theories and methods presented in this book.

Iterative Functional Equations

Iterative Functional Equations Author Marek Kuczma
ISBN-10 0521355613
Release 1990-07-27
Pages 552
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A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.

Functional Equations and Inequalities in Several Variables

Functional Equations and Inequalities in Several Variables Author Stefan Czerwik
ISBN-10 9789814489508
Release 2002-05-14
Pages 420
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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. Contents:Functional Equations and Inequalities in Linear Spaces:Linear Spaces and Semilinear TopologyConvex FunctionsCauchy's Exponential EquationPolynomial Functions and Their ExtensionsQuadratic MappingsQuadratic Equation on an IntervalUlam–Hyers–Rassias Stability of Functional Equations:Additive Cauchy EquationMultiplicative Cauchy EquationJensen's Functional EquationGamma Functional EquationStability of Homogeneous MappingsStability of Functional Equations in Function SpacesStability in the Lipschitz NormsRound-off Stability of IterationsFunctional Equations in Set-Valued Functions:Cauchy's Set-Valued Functional EquationPexider's Functional EquationSubadditive Set-Valued FunctionsHahn–Banach Type Theorem and ApplicationsSubquadratic Set-Valued FunctionsIteration Semigroups of Set-Valued Functions Readership: Graduate students, researchers and academics in the field of analysis and differential equations. Keywords:Functional Equations;Inequalities;Several Variables;Semilinear Topology;Convex Functions;Quadratic Equation;Stability;Lipschitz Norms;Set-Valued FunctionsReviews:“Particularly valuable (Part III) is a systematic discussion of set-valued functional equations.”Mathematical Reviews “Written by an expert in domain, the book is an excellent tool for any reader interested to get an idea about the basic results and the latest research directions in the field of functional equations.”Studia Universitatis Babes-Bolyai, Series Mathematica

Stability of Vector Differential Delay Equations

Stability of Vector Differential Delay Equations Author Michael I. Gil’
ISBN-10 9783034805773
Release 2013-02-14
Pages 259
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Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states. The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the Aizerman-Myshkis problem and generalized Hill theory of periodic systems. The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.

Stability of Functional Equations in Random Normed Spaces

Stability of Functional Equations in Random Normed Spaces Author Yeol Je Cho
ISBN-10 9781461484776
Release 2013-08-27
Pages 246
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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 in Several Variables

Functional Equations in Several Variables Author J. Aczel
ISBN-10 0521352762
Release 1989
Pages 462
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Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.

Fundamentals of Geophysical Hydrodynamics

Fundamentals of Geophysical Hydrodynamics Author Felix V. Dolzhansky
ISBN-10 9783642310348
Release 2012-10-26
Pages 274
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This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold's approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation. This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author's highly acclaimed work in Moscow's Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.

Mathematical Analysis Approximation Theory and Their Applications

Mathematical Analysis  Approximation Theory and Their Applications Author Themistocles Rassias
ISBN-10 9783319312811
Release 2016-06-03
Pages 741
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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.

Functional Equations and Inequalities

Functional Equations and Inequalities Author Themistocles RASSIAS
ISBN-10 9789401143417
Release 2012-12-06
Pages 336
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Functional Equations and Inequalities has been writing in one form or another for most of life. You can find so many inspiration from Functional Equations and Inequalities also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Functional Equations and Inequalities book for free.