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Stability of Functional Equations in Several Variables

  • Book
  • © 1998

Overview

Authors:
  1. Donald H. Hyers
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  2. George Isac

    1. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada

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  3. Themistocles M. Rassias

    1. Department of Mathematics, National Technical University of Athens, Athens, Greece

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 34)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Prologue

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 1-10

  3. Introduction

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 11-14

  4. Approximately Additive and Approximately Linear Mappings

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 15-44

  5. Stability of the Quadratic Functional Equation

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 45-77

  6. Generalizations. The Method of Invariant Means

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 78-101

  7. Approximately Multiplicative Mappings. Superstability

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 102-131

  8. The Stability of Functional Equations for Trigonometric and Similar Functions

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 132-154

  9. Functions with Bounded nth Differences

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 155-165

  10. Approximately Convex Functions

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 166-179

  11. Stability of the Generalized Orthogonality Functional Equation

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 180-203

  12. Stability and Set-Valued Functions

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 204-231

  13. Stability of Stationary and Minimum Points

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 232-245

  14. Functional Congruences

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 246-276

  15. Quasi-Additive Functions and Related Topics

    • Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 277-289

  16. Back Matter

    Pages 290-318
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Keywords

About this book

The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de­ veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre­ sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa­ tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co­ author and friend Professor Donald H. Hyers passed away.

Reviews

"…The book under review is an exhaustive presentation of the results in the field, not called Hyers-Ulam stability. It contains chapters on approximately additive and linear mappings, stability of the quadratic functional equation, approximately multiplicative mappings, functions with bounded differences, approximately convex functions. The book is of interest not only for people working in functional equations but also for all mathematicians interested in functional analysis."

–Zentralblatt Math

"Contains survey results on the stability of a wide class of functional equations and therefore, in particular, it would be interesting for everyone who works in functional equations theory as well as in the theory of approximation."

–Mathematical Reviews

Authors and Affiliations

  • Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada

    George Isac

  • Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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