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9780817640248

Stability of Functional Equations in Several Variables

by ; ;
  • ISBN13:

    9780817640248

  • ISBN10:

    081764024X

  • Format: Hardcover
  • Copyright: 1998-06-01
  • Publisher: Birkhauser

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Summary

The notion of stability of functional equations has been an area of revision and development for the past 20 years, having its origins more than half a century ago when S. Ulam posed the fundamental problem and D. H. Hyers gave the first significant partial solution. This volume is unique in that (to date) none exists as a comprehensive examination to the subject.The authors present both classical results and their original research in an integrated and self-contained fashion. Apart from the main topic of the stability of certain functional equations, related problems are discussed. These include the stability of the convex functional inequality and the stability of minimum points. The techniques used require some basic knowledge of functional analysis, algebra, and topology.The text could be used in graduate seminars or by researchers in the field.

Table of Contents

Preface vii
Prologue 1(10)
Introduction
11(4)
Approximately Additive and Approximately Linear Mappings
15(30)
Stability of the Quadratic Functional Equation
45(33)
Generalizations. The Method of Invariant Means
78(24)
Approximately Multiplicative Mappings. Superstability
102(30)
The Stability of Functional Equations for Trigonometric and Similar Functions
132(23)
Functions with Bounded nth Differences
155(11)
Approximately Convex Functions
166(14)
Stability of the Generalized Orthogonality Functional Equation
180(24)
Stability and Set-Valued Functions
204(28)
Stability of Stationary and Minimum Points
232(14)
Functional Congruences
246(31)
Quasi-Additive Functions and Related Topics
277(13)
References 290(17)
Index 307

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