### 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 language | English |
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Pages (from-to) | 651-666 |

Number of pages | 16 |

Journal | Publicationes Mathematicae |

Volume | 58 |

Issue number | 4 |

Publication status | Published - Dec 1 2001 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)