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Stability of Functional Equations in Several Variables

  • Donald H. Hyers
  • George Isac
  • Themistocles M. Rassias

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

Table of contents

  1. Front Matter
    Pages i-vii
  2. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 1-10
  3. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 11-14
  4. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 15-44
  5. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 45-77
  6. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 78-101
  7. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 102-131
  8. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 132-154
  9. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 155-165
  10. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 166-179
  11. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 180-203
  12. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 204-231
  13. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 232-245
  14. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 246-276
  15. Donald H. Hyers, George Isac, Themistocles M. Rassias
    Pages 277-289
  16. Back Matter
    Pages 290-318

About this book

Introduction

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.

Keywords

Algebra Invariant Mathematics Topology Variable calculus equation function functional analysis

Authors and affiliations

  • Donald H. Hyers
  • George Isac
    • 1
  • Themistocles M. Rassias
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information