Rassias Themistocles M. Functional Equations and Inequalities

Springer, 2000. — 336 p. — ISBN: 9789401058698.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.On the Stability of a Functional Equation for Generalized Trigonometric Functions
Roman BadoraSome Notes on Two-Scale Difference Equations
Lothar Berg, Gerlind PlonkaSome Demand Functions in a Duopoly Market with Advertising
Enrique Castillo, Jose Maria Sarabia, Ana Mercedes GonzalezSolutions of a Functional Inequality in a Special Class of Functions
Marek CzerniOn Dependence of Lipschitzian Solutions of Nonlinear Functional Inequality on an Arbitrary Function
Marek CzerniThe Problem of Expressibility in Some Extensions of Free Groups
Valeriĭ FaĭzievOn a Pythagorean Functional Equation Involving Certain Number Fields
J. L. Garcia-Roig, J. SalillasOn a Conditional Cauchy Functional Equation Involving Cubes
J. L. Garcia-Roig, Emma Martín-GutiérrezHyers-Ulam Stability of HosszÚ’s Equation
P. GăvruţăThe Functional Equation of the Square Root Spiral
Konrad J. Heuvers, Daniel S. Moak, Blake BoursawOn the Superstability of the Functional Equation f(xy) = f(x)y
Soon-Mo JungReplicativity and Function Spaces
Hans-Heinrich KairiesNormal Distributions and the Functional Equation f(x + y)g(x - y) = f(x)f(y)g(x)g(-y)
P. KannappanOn The Polynomial-Like Iterative Functional Equation
Janusz Matkowski, Weinian ZhangDistribution of Zeros and Inequalities for Zeros of Algebraic Polynomials
Gradimir V. Milovanović, Themistocles M. RassiasA Functional Definition of Trigonometric Functions
Nicolae N. NeamţuA Qualitative Study of Lobachevsky’s Complex Functional Equation
Nicolae N. NeamţuSmooth Solutions of an Iterative Functional Equation
Jian-Guo Si, Wei-Nian Zhang, Sui-Sun ChengSet-Valued Quasiconvex Functions and their Constant Selections
Wilhelmina Smajdor
Pages 233-247Entire Solutions of the Hille-Type Functional Equation
Andrzej Smajdor, Wilhelmina SmajdorUlam’s Problem, Hyers’s Solution — and to Where They Led
László SzékelyhidiA Separation Lemma for the Construction of Finite Sums Decompositions
Wolfgang TutschkeAleksandrov Problem and Mappings which Preserve Distances
Shuhuang XiangOn Some Subclasses of Harmonic Functions
Sibel Yalçin, Metin Öztürk, Mümin Yamankaradeniz