### Abstract

The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarević means, i.e., to solve the functional equation (Formula presented.)where (Formula presented.) are unknown continuous functions such that g, k are nowhere zero on I, the ratio functions f / g, h / k are strictly monotone on I, and (Formula presented.) are constants different from each other. By the main result of this paper, the solutions of the above invariance equation can be expressed either in terms of hyperbolic functions or in terms of trigonometric functions and an additional weight function. For the necessity part of this result, we will assume that (Formula presented.) are four times continuously differentiable.

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

Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | Aequationes Mathematicae |

DOIs | |

Publication status | Accepted/In press - May 11 2018 |

### Fingerprint

### Keywords

- Bajraktarević mean
- Functional equation
- Invariance equation
- Invariant mean

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Aequationes Mathematicae*, 1-21. https://doi.org/10.1007/s00010-018-0560-9

**On the invariance equation for two-variable weighted nonsymmetric Bajraktarević means.** / Páles, Z.; Zakaria, Amr.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the invariance equation for two-variable weighted nonsymmetric Bajraktarević means

AU - Páles, Z.

AU - Zakaria, Amr

PY - 2018/5/11

Y1 - 2018/5/11

N2 - The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarević means, i.e., to solve the functional equation (Formula presented.)where (Formula presented.) are unknown continuous functions such that g, k are nowhere zero on I, the ratio functions f / g, h / k are strictly monotone on I, and (Formula presented.) are constants different from each other. By the main result of this paper, the solutions of the above invariance equation can be expressed either in terms of hyperbolic functions or in terms of trigonometric functions and an additional weight function. For the necessity part of this result, we will assume that (Formula presented.) are four times continuously differentiable.

AB - The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarević means, i.e., to solve the functional equation (Formula presented.)where (Formula presented.) are unknown continuous functions such that g, k are nowhere zero on I, the ratio functions f / g, h / k are strictly monotone on I, and (Formula presented.) are constants different from each other. By the main result of this paper, the solutions of the above invariance equation can be expressed either in terms of hyperbolic functions or in terms of trigonometric functions and an additional weight function. For the necessity part of this result, we will assume that (Formula presented.) are four times continuously differentiable.

KW - Bajraktarević mean

KW - Functional equation

KW - Invariance equation

KW - Invariant mean

UR - http://www.scopus.com/inward/record.url?scp=85046785355&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046785355&partnerID=8YFLogxK

U2 - 10.1007/s00010-018-0560-9

DO - 10.1007/s00010-018-0560-9

M3 - Article

AN - SCOPUS:85046785355

SP - 1

EP - 21

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

ER -