On the local and global comparison of generalized Bajraktarevic means

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Pales, Zsolt¹  Zakaria, Amr² 

[1] Univ Debrecen, Inst Math, Pf 400, H-4002 Debrecen, Hungary

[2] Ain Shams Univ, Fac Educ, Dept Math, Cairo 11341, Egypt

关键词: Generalized integral mean;    Quasi-arithmetic mean;    Bajraktarevic mean;    Gini mean;    Comparison problem;    Chebyshev system;   

DOI  :  10.1016/j.jmaa.2017.05.073

来源: Elsevier

【 摘 要 】

Given two continuous functions f, g : I -> R such that g is positive and f/g is strictly monotone, a measurable space (T, A), a measurable family of d-variable means m : I-d x T -> I, and a probability measure mu on the measurable sets A, the d-variable mean M-f,M-g,M-m:mu : I-d -> I is defined by M-f,M-g,M-m:mu (x) :=(f/g)(-1) (integral(T) f(m(x(1) , . . . ,x(d,)t)) d mu(t)/integral(T) g(m(x(1) , . . . ,x(d,)t)) d mu(t)) (x = (x(1), . . . ,x(d)) is an element of I-d). The aim of this paper is to study the local and global comparison problem of these means, i.e., to find conditions for the generating functions (f, g) and (h, k), for the families of means m and n, and for the measures mu, nu such that the comparison inequality M-f,M-g,M-m:mu (x) <= M-h,M-k,M-n;nu(X) (x is an element of I-d) be satisfied. (C) 2017 Elsevier Inc. All rights reserved.

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