Estimates to the stability of functional equations

Attila Gilányi, Zoltán Kaiser, Zsolt Páles

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Given a function f mapping a groupoid (X,) into a metric groupoid (Y,*,d) and satisfying the inequality d(f(x y),f(x)*f(y))≤ ε(x,y)\quad (x,y ∈ X), the problem of stability in the sense of Hyers-Ulam is to construct a solution g of the functional equation g(x y) = g(x)*g(y) (x,y ∈ X) and to obtain estimates for the pointwise distance between g and f. Applying the so-called direct method, the stability problem for more general functional equations is also investigated.

Original languageEnglish
Pages (from-to)125-143
Number of pages19
JournalAequationes Mathematicae
Volume73
Issue number1-2
DOIs
Publication statusPublished - Mar 1 2007

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Keywords

  • Cauchy's functional equation
  • Hyers iteration
  • Power-symmetric groupoids
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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