Functional Equations and Inequalities

ISBN-13: 9789401058698 / Angielski / Miękka / 2012 / 336 str.

Themistocles M. Rassias

Opis

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 Hosszu'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."

Spis treści

Preface. On the Stability of a Functional Equation for Generalized Trigonometric Functions; R. Badora. Some Notes on Two-Scale Difference Equations; L. Berg, G. Plonka. Some Demand Functions in a Duopoly Market with Advertising; E. Castillo, et al. Solutions of a Functional Inequality in a Special Class of Functions; M. Czerni. On Dependence of Lipschitzian Solutions of Nonlinear Functional Inequality on an Arbitrary Function; M. Czerni. The Problem of Expressibility in Some Extensions of Free Groups; V. Faiziev. On a Pythagorean Functional Equation Involving Certain Number Fields; J.L. Garcia-Roig, J. Salillas. On a Conditional Cauchy Functional Equation Involving Cubes; J.L. Garcia-Roig, E. Martín-Gutiérrez. Hyers-Ulam Stability of Hosszú's Equation; P. Gavruta. The Functional Equation of the Square Root Spiral; K.J. Heuvers, et al. On the Superstability of the Functional Equation f(xy)=f(x)y; S.-M. Jung. Replicativity and Function Spaces; H.-H. Kairies. Normal Distributions and the Functional Equation f(x+y) g(x-y) = f(x) f(y) g(x) g(-y); P.L. Kannappan. On the Polynomial-Like Iterative Functional Equation; J. Matkowski, W. Zhang. Distribution of Zeros and Inequalities for Zeros of Algebraic Polynomials; G.V. Milovanovic, T.M. Rassias. A Functional Definition of Trigonometric Functions; N.N. Neamtu. A Qualitative Study of Lobachevksy's Complex Functional Equation; N.N. Neamtu. Smooth Solutions of an Iterative Functional Equation; J.-G. Si, et al. Set-Valued Quasiconvex Functions and their Constant Selections; W. Smajdor. Entire Solution of the Hille-type Functional Equation; A. Smajdor, W. Smajdor. Ulam's Problem, Hyer's Solution - and to Where they Led; L. Székelyhidi. ASeparation Lemma for the Construction of Finite Sums Decompositions; W. Tutschke. Aleksandrov Problem and Mappings which Preserve Distances; S. Xiang. On Some Subclasses of Harmonic Functions; S. Yalçin, et al. Index.