Functional Equations And Inequalities In Several Variables
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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.
Stability of Functional Equations in Several Variables by D.H. Hyers,G. Isac,Themistocles Rassias Pdf
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 in Several Variables by J. Aczél,J. Dhombres Pdf
This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum.
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
Functional Equations and Inequalities by Themistocles M. Rassias Pdf
Functional Equations andInequalities provides an extensive studyofsome of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition oftrigonometric functions, the functional equation ofthe square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution ofzeros and inequalities for zeros of algebraic polynomials, a qualitative study ofLobachevsky's complex functional equation, functional inequalities in special classesoffunctions, replicativity and function spaces, normal distributions, some difference equations, finite sums decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problem 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 Hosszil's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. It is a pleasureto express my deepest appreciationto all the mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staffofKluwer Academic Publishers. June 2000 Themistocles M. Rassias xi ON THE STABILITY OF A FUNCTIONAL EQUATION FOR GENERALIZED TRIGONOMETRIC FUNCTIONS ROMAN BADORA lnstytut Matematyki, Uniwersytet Sli;ski, ul. Bankowa 14, PL-40-007 Katowice, Poland, e-mail: robadora@gate. math. us. edu. pl Abstract. In the present paper the stability result concerning a functional equation for generalized trigonometric functions is presented. Z.
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.
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.
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.
Regularity Properties of Functional Equations in Several Variables by Antal Járai Pdf
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
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)
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.
Functional Equations on Hypergroups by L szl¢ Szkelyhidi Pdf
The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate OC marriageOCO where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods OCo and, sometimes, a new world of unexpected difficulties.
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.
