Hyers - Ulam stability of the Cauchy functional equation on square-symmetric groupoids

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Abstract

The stability of the functional equation f (x ◇ y)= f (x) * f (y) (x, y ∈ X) is investigated, where f : X → Y and ◇, * are square-symmetric operations on the sets X and Y, respectively. The results presented include and generalize the classical theorem of Hyers obtained on the stability of the Cauchy functional equation in 1941.

Original languageEnglish
Pages (from-to)651-666
Number of pages16
JournalPublicationes Mathematicae
Volume58
Issue number4
Publication statusPublished - Dec 1 2001

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Keywords

  • Cauchy functional equation
  • Hyers - Ulam stability
  • Square-symmetric groupoid

ASJC Scopus subject areas

  • Mathematics(all)

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