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Prologue

  • Donald H. Hyers
  • George Isac
  • Themistocles M. Rassias
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 34)

Abstract

To quote S.M. Ulam (1960) (page 63)1 for very general functional equations, one can ask the following question. When is it true that the solution of an equation differing slightly from a given one, must of necessity be close to the solution of the given equation? Similarly, if we replace a given functional equation by a functional inequality, when can one assert that the solutions of the inequality lie near the solutions of the strict equation? The present work is designed to provide an introduction to the formulation and solution of such problems by examination of various researches most of which has been carried out during the last two decades.

Keywords

Functional Equation Topological Vector Space Stability Theorem Commutative Semigroup Functional Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

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

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