### Abstract

The stability of the functional equation f(x o y) = H(f(x), f(y)) (x, y ε S) is investigated, where H is a homogeneous function and o is a square- symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Original language | English |
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Pages (from-to) | 12772-12775 |

Number of pages | 4 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 95 |

Issue number | 22 |

DOIs | |

Publication status | Published - Oct 27 1998 |

### ASJC Scopus subject areas

- General

## Cite this

Páles, Z., Volkmann, P., & Luce, R. D. (1998). Hyers-Ulam stability of functional equations with a square-symmetric operation.

*Proceedings of the National Academy of Sciences of the United States of America*,*95*(22), 12772-12775. https://doi.org/10.1073/pnas.95.22.12772