Stability of Functional Equations in Several Variables / Edition 1

Stability of Functional Equations in Several Variables / Edition 1

by D.H. Hyers, G. Isac, Themistocles M. Rassias
     
 

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

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Overview

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.

Product Details

ISBN-13:
9780817640248
Publisher:
Birkhauser Verlag
Publication date:
09/28/1998
Series:
Progress in Nonlinear Differential Equations and Their Applications Series, #32
Edition description:
1998
Pages:
318
Product dimensions:
9.21(w) x 6.14(h) x 0.75(d)

Table of Contents

Prologue.- 1. Introduction.- 2. Approximately Additive and Approximately Linear Mappings.- 3. Stability of the Quadratic Functional Equation.- 4. Generalizations. The Method of Invariant Means.- 5. Approximately Multiplicative Mappings. Superstability.- 6. The Stability of Functional Equations for Trigonometric and Similar Functions.- 7. Functions with Bounded nth Differences.- 8. Approximately Convex Functions.- 9. Stability of the Generalized Orthogonality Functional Equation.- 10. Stability and Set-Valued Functions.- 11. Stability of Stationary and Minimum Points.- 12. Functional Congruences.- 13. Quasi-Additive Functions and Related Topics.- References.

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