Author: Palaniappan Kannappan
Publisher: Springer Science & Business Media
ISBN: 0387894926
Category : Mathematics
Languages : en
Pages : 817
Get Book
Book Description
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
ISBN: 940170225X
Category : Mathematics
Languages : en
Pages : 221
Get Book
Book Description
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: Stefan Czerwik
Publisher: World Scientific
ISBN: 9789810248376
Category : Mathematics
Languages : en
Pages : 424
Get Book
Book Description
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: B. Forte
Publisher: Springer Science & Business Media
ISBN: 3642110045
Category : Mathematics
Languages : en
Pages : 425
Get Book
Book Description
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
ISBN: 1493912461
Category : Mathematics
Languages : en
Pages : 555
Get Book
Book Description
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: J. Aczél
Publisher: Academic Press
ISBN: 0080955258
Category : Computers
Languages : en
Pages : 534
Get Book
Book Description
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.
Author: John Michael Rassias
Publisher: World Scientific Publishing Company
ISBN: 9813147628
Category :
Languages : en
Pages : 396
Get Book
Book Description
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: Themistocles RASSIAS
Publisher: Springer Science & Business Media
ISBN: 9401143412
Category : Mathematics
Languages : en
Pages : 335
Get Book
Book Description
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: George A. Anastassiou
Publisher: Springer Nature
ISBN: 3030289508
Category : Mathematics
Languages : en
Pages : 746
Get Book
Book Description
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: Janusz Brzdęk
Publisher: Springer
ISBN: 331961732X
Category : Mathematics
Languages : en
Pages : 354
Get Book
Book Description
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.
