### 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 - 2001 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Hyers - Ulam stability of the Cauchy functional equation on square-symmetric groupoids.** / Páles, Z.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 58, no. 4, pp. 651-666.

}

TY - JOUR

T1 - Hyers - Ulam stability of the Cauchy functional equation on square-symmetric groupoids

AU - Páles, Z.

PY - 2001

Y1 - 2001

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

UR - http://www.scopus.com/inward/record.url?scp=0035661343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035661343&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035661343

VL - 58

SP - 651

EP - 666

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 4

ER -