Functional equations and inequalities with applications

Palaniappan Kannappan (auth.)0387894918, 9780387894911

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.

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.

The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition.

Table of contents :
Front Matter….Pages 1-21
Basic Equations: Cauchy and Pexider Equations….Pages 1-83
Matrix Equations….Pages 85-103
Trigonometric Functional Equations….Pages 105-219
Quadratic Functional Equations….Pages 221-245
Characterization of Inner Product Spaces….Pages 247-294
Stability….Pages 295-327
Characterization of Polynomials….Pages 329-357
Nondifferentiable Functions….Pages 359-370
Characterization of Groups, Loops, and Closure Conditions….Pages 371-401
Functional Equations from Information Theory….Pages 403-467
Abel Equations and Generalizations….Pages 469-492
Regularity Conditions—Christensen Measurability….Pages 493-509
Difference Equations….Pages 511-535
Characterization of Special Functions….Pages 537-561
Miscellaneous Equations….Pages 563-605
General Inequalities….Pages 607-667
Applications….Pages 669-756
Back Matter….Pages 1-52