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

Z. Páles, Amr Zakaria

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-21
Number of pages21
JournalAequationes Mathematicae
DOIs
Publication statusAccepted/In press - May 11 2018

Fingerprint

Invariance
Hyperbolic functions
Weighted Mean
Hyperbolic function
Circular function
Continuously differentiable
Weight Function
Functional equation
Monotone
Continuous Function
Strictly
Unknown
Zero

Keywords

  • Bajraktarević mean
  • Functional equation
  • Invariance equation
  • Invariant mean

ASJC Scopus subject areas

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

Cite this

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

In: Aequationes Mathematicae, 11.05.2018, p. 1-21.

Research output: Contribution to journalArticle

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