### Abstract

The paper deals with the equality problem of quasi-arithmetic and Lagrangian means which is to determine all pairs of continuous strictly monotone functions Φ,Ψ:I→R such that, for all x,y∈I,. holds. The main result of the paper shows that there are 6 different cases of equality.

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

Pages (from-to) | 86-96 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 382 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1 2011 |

### Fingerprint

### Keywords

- Equality problem
- Lagrangian mean
- Quasi-arithmetic mean

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**On the equality of quasi-arithmetic and Lagrangian means.** / Páles, Z.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 382, no. 1, pp. 86-96. https://doi.org/10.1016/j.jmaa.2011.04.033

}

TY - JOUR

T1 - On the equality of quasi-arithmetic and Lagrangian means

AU - Páles, Z.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - The paper deals with the equality problem of quasi-arithmetic and Lagrangian means which is to determine all pairs of continuous strictly monotone functions Φ,Ψ:I→R such that, for all x,y∈I,. holds. The main result of the paper shows that there are 6 different cases of equality.

AB - The paper deals with the equality problem of quasi-arithmetic and Lagrangian means which is to determine all pairs of continuous strictly monotone functions Φ,Ψ:I→R such that, for all x,y∈I,. holds. The main result of the paper shows that there are 6 different cases of equality.

KW - Equality problem

KW - Lagrangian mean

KW - Quasi-arithmetic mean

UR - http://www.scopus.com/inward/record.url?scp=79956120827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956120827&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2011.04.033

DO - 10.1016/j.jmaa.2011.04.033

M3 - Article

AN - SCOPUS:79956120827

VL - 382

SP - 86

EP - 96

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -