### Abstract

In this paper, the functional equation f(px + (1 - p)y) + f((1 - p)x + py) = f(x) + f(y), (x,y \in I) is considered, where 0 < p < 1 is a fixed parameter and f: I → R is an unknown function. The equivalence of this and Jensen's functional equation is completely characterized in terms of the algebraic properties of the parameter p. As an application, solutions of certain functional equations involving four weighted arithmetic means are also determined.

Original language | English |
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Pages (from-to) | 79-87 |

Number of pages | 9 |

Journal | Acta Mathematica Hungarica |

Volume | 116 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jul 1 2007 |

### Keywords

- Biadditive function
- Jensen-affine function
- Linear functional equation
- P-Wright affine function

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Daróczy, Z., Lajkó, K., Lovas, R. L., Maksa, G., & Páles, Z. (2007). Functional equations involving means.

*Acta Mathematica Hungarica*,*116*(1-2), 79-87. https://doi.org/10.1007/s10474-007-5296-2