On the equality of generalized quasi-arithmetic means

Zita Makó, Z. Páles

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Given a continuous strictly monotone function φ : I → ℝ and a probability measure μ on the Borel subsets of [0,1], the two variable mean Mφ,μ : I2 → I is defined by M φ,μ(x, y) := φ-1(∫01 φ(tx + (1 - t)y)dμ(t)) (x, y ε I. This class of means includes quasi-arithmetic as well as Lagrangian means. The aim of this paper is to study their equality problem, i.e., to characterize those pairs (φ,μ) and (ψ, ν) such that Mφ,μ(x, y) = Mψ,ν(x, y) (x,t ε I holds. Under at most fourth-order differentiability assumptions for the unknown functions φ and ψ, a complete description of the solution set of the above functional equation is obtained.

Original languageEnglish
Pages (from-to)407-440
Number of pages34
JournalPublicationes Mathematicae
Volume72
Issue number3-4
Publication statusPublished - 2008

Fingerprint

Quasi-arithmetic Mean
Equality
Monotone Function
Differentiability
Solution Set
Probability Measure
Functional equation
Fourth Order
Strictly
Unknown
Subset
Class

Keywords

  • Equality problem
  • Generalized quasi-arithmetic means

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the equality of generalized quasi-arithmetic means. / Makó, Zita; Páles, Z.

In: Publicationes Mathematicae, Vol. 72, No. 3-4, 2008, p. 407-440.

Research output: Contribution to journalArticle

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