Ebook: Functional Equations and Inequalities

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.

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Content:
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 Hossz?’s Equation....Pages 105-110
The Functional Equation of the Square Root Spiral....Pages 111-117
Replicativity and Function Spaces....Pages 119-124
On The Polynomial-Like Iterative Functional Equation....Pages 125-138
Distribution of Zeros and Inequalities for Zeros of Algebraic Polynomials....Pages 139-144
A Functional Definition of Trigonometric Functions....Pages 145-170
A Qualitative Study of Lobachevsky’s Complex Functional Equation....Pages 171-204
Smooth Solutions of an Iterative Functional Equation....Pages 205-213
Set-Valued Quasiconvex Functions and their Constant Selections....Pages 215-220
Entire Solutions of the Hille-Type Functional Equation....Pages 221-232
Ulam’s Problem, Hyers’s Solution — and to Where They Led....Pages 233-247
A Separation Lemma for the Construction of Finite Sums Decompositions....Pages 249-258
Aleksandrov Problem and Mappings which Preserve Distances....Pages 259-285
On Some Subclasses of Harmonic Functions....Pages 287-296
Back Matter....Pages 297-323
....Pages 325-331