### Abstract

In this note we solve the equality problem of weighted quasi-arithmetic means of two variables in the particular case when one of the weight functions is constant. As an application, we determine all those weighted arithmetic means that are also quasi-arithmetic. No differentiability conditions on the unknown functions are assumed.

Original language | English |
---|---|

Pages (from-to) | 154-159 |

Number of pages | 6 |

Journal | Aequationes Mathematicae |

Volume | 67 |

Issue number | 1-2 |

Publication status | Published - Mar 2004 |

### Fingerprint

### Keywords

- Functional equation
- Quasi-arithmetic mean
- Regularity theorem
- Weighted arithmetic mean

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Aequationes Mathematicae*,

*67*(1-2), 154-159.

**On two-variable means with variable weights.** / Daróczy, Zoltán; Maksa, Gyula; Páles, Zsolt.

Research output: Contribution to journal › Article

*Aequationes Mathematicae*, vol. 67, no. 1-2, pp. 154-159.

}

TY - JOUR

T1 - On two-variable means with variable weights

AU - Daróczy, Zoltán

AU - Maksa, Gyula

AU - Páles, Zsolt

PY - 2004/3

Y1 - 2004/3

N2 - In this note we solve the equality problem of weighted quasi-arithmetic means of two variables in the particular case when one of the weight functions is constant. As an application, we determine all those weighted arithmetic means that are also quasi-arithmetic. No differentiability conditions on the unknown functions are assumed.

AB - In this note we solve the equality problem of weighted quasi-arithmetic means of two variables in the particular case when one of the weight functions is constant. As an application, we determine all those weighted arithmetic means that are also quasi-arithmetic. No differentiability conditions on the unknown functions are assumed.

KW - Functional equation

KW - Quasi-arithmetic mean

KW - Regularity theorem

KW - Weighted arithmetic mean

UR - http://www.scopus.com/inward/record.url?scp=2142776645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142776645&partnerID=8YFLogxK

M3 - Article

VL - 67

SP - 154

EP - 159

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 1-2

ER -