FUNCTIONAL EQUATIONS AND INEQUALITIES WITH APPLICATIONS

It is natural to ask what a functional equation is. But there is no easy satisfactory answer to this question. While such concepts as element, relation, mapping, operation, etc., are well defined in set theory, the principal concept set is an undefined term. It is not considered as an impediment for the growth, development, and usefulness of set theory. We are going to follow this idea and consider functional equations as an undefined concept. This is not going to be a severe roadblock to understanding, appreciating, and contributing to the growth and development of this fascinating area. As in set theory, we hope the reader will get a general insight of what this theory is about.

CONTENTS

Preface

1. Basic Equations: Cauchy and Pexider Equations
2. Matrix Equations
3. Trigonometric Functional Equations
4. Quadratic Functional Equations
5. Characterization of Inner Product Spaces
6. Stability
7. Characterization of Polynomials
8. Nondifferentiable Functions
9. Characterization of Groups, Loops, and Closure Conditions
10. Functional Equations from Information Theory
11. Abel Equations and Generalizations
12. Regularity Conditions—Christensen Measurability
13. Difference Equations
14. Characterization of Special Functions
15. Miscellaneous Equations
16. General Inequalities
17. Applications

List of Symbols
Bibliography
Author Index Subject Index

Páginas : 840
Peso : 6mb.
Formato : PDF.
Edición : 1 edition
Año de Publicación :2009
ISBN : 978-0387894911
Editorial : Springer
Autor Palaniappan Kannappan

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