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

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40 Citations (Scopus)

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 - 2001

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Cauchy Functional Equation
Hyers-Ulam Stability
Groupoids
Functional equation
Generalise
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Hyers - Ulam stability of the Cauchy functional equation on square-symmetric groupoids",
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.",
keywords = "Cauchy functional equation, Hyers - Ulam stability, Square-symmetric groupoid",
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AU - Páles, Z.

PY - 2001

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N2 - 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.

AB - 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.

KW - Cauchy functional equation

KW - Hyers - Ulam stability

KW - Square-symmetric groupoid

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