Functional Equations and Inequalities

✍ Scribed by Themistocles M. Rassias (auth.)

• Publisher: Springer Netherlands
• Year: 2000
• Tongue: English
• Leaves: 334
• Series: Mathematics and Its Applications 518
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
On the Stability of a Functional Equation for Generalized Trigonometric Functions....Pages 1-5
Some Notes on Two-Scale Difference Equations....Pages 7-29
Some Demand Functions in a Duopoly Market with Advertising....Pages 31-54
Solutions of a Functional Inequality in a Special Class of Functions....Pages 55-63
On Dependence of Lipschitzian Solutions of Nonlinear Functional Inequality on an Arbitrary Function....Pages 65-75
The Problem of Expressibility in Some Extensions of Free Groups....Pages 77-90
On a Pythagorean Functional Equation Involving Certain Number Fields....Pages 91-95
On a Conditional Cauchy Functional Equation Involving Cubes....Pages 97-104
Hyers-Ulam Stability of HosszÚ’s Equation....Pages 105-110
The Functional Equation of the Square Root Spiral....Pages 111-117
On the Superstability of the Functional Equation f(x y ) = f(x) y ....Pages 119-124
Replicativity and Function Spaces....Pages 125-138
Normal Distributions and the Functional Equation f(x + y)g(x - y) = f(x)f(y)g(x)g(-y) ....Pages 139-144
On The Polynomial-Like Iterative Functional Equation....Pages 145-170
Distribution of Zeros and Inequalities for Zeros of Algebraic Polynomials....Pages 171-204
A Functional Definition of Trigonometric Functions....Pages 205-213
A Qualitative Study of Lobachevsky’s Complex Functional Equation....Pages 215-220
Smooth Solutions of an Iterative Functional Equation....Pages 221-232
Set-Valued Quasiconvex Functions and their Constant Selections....Pages 233-247
Entire Solutions of the Hille-Type Functional Equation....Pages 249-258
Ulam’s Problem, Hyers’s Solution — and to Where They Led....Pages 259-285
A Separation Lemma for the Construction of Finite Sums Decompositions....Pages 287-296
Aleksandrov Problem and Mappings which Preserve Distances....Pages 297-323
On Some Subclasses of Harmonic Functions....Pages 325-331
Back Matter....Pages 333-336

✦ Subjects

Difference and Functional Equations; Approximations and Expansions; Functional Analysis; Functions of a Complex Variable; Partial Differential Equations