Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4620433 | Journal of Mathematical Analysis and Applications | 2009 | 16 Pages |
Abstract
The aim of this paper is to find those pairs of generalized quasi-arithmetic means on an open real interval I for which the arithmetic mean is invariant, i.e., to characterize those continuous strictly monotone functions φ,ψ:I→Rφ,ψ:I→R and Borel probability measures μ,νμ,ν on the interval [0,1][0,1] such thatφ−1(∫01φ(tx+(1−t)y)dμ(t))+ψ−1(∫01ψ(tx+(1−t)y)dν(t))=x+y(x,y∈I) holds. Under at most fourth-order differentiability assumptions and certain nondegeneracy conditions on the measures, the main results of this paper show that there are three classes of the solutions φ,ψφ,ψ: they are equivalent either to linear, or to exponential or to power functions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zita Makó, Zsolt Páles,