### 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 |
---|---|

Pages (from-to) | 363-377 |

Number of pages | 15 |

Journal | Publicationes Mathematicae |

Volume | 62 |

Issue number | 3-4 |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

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

**On functional equations involving means.** / Daróczy, Zoltán; Páles, Z.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 62, no. 3-4, pp. 363-377.

}

TY - JOUR

T1 - On functional equations involving means

AU - Daróczy, Zoltán

AU - Páles, Z.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Functional equation

KW - Matkowski-Sutô problem

KW - Stolarsky means

KW - Weighted quasi-arithmetic mean

UR - http://www.scopus.com/inward/record.url?scp=0038585088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038585088&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0038585088

VL - 62

SP - 363

EP - 377

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -