### Abstract

The main results of the paper concern functional equations of the form f(M(x,y))(g(y) - g(x)) = μ(f(x)g(y) - f(y)g(x)) (x, y ∈ I), where f and g are continuous functions defined on an open interval I and M is a strict two variable mean on I. As an application, a generalization of the so-called Matkowski-Sutô problem for weighted two variable quasi-arithmetic means is solved under first-order continuous differentiability assumptions.

Original language | English |
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Pages (from-to) | 363-377 |

Number of pages | 15 |

Journal | Publicationes Mathematicae |

Volume | 62 |

Issue number | 3-4 |

Publication status | Published - Jan 1 2003 |

### Keywords

- Functional equation
- Matkowski-Sutô problem
- Stolarsky means
- Weighted quasi-arithmetic mean

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Daróczy, Z., & Páles, Z. (2003). On functional equations involving means.

*Publicationes Mathematicae*,*62*(3-4), 363-377.