An invariance of geometric mean with respect to generalized quasi-arithmetic means

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Zhang, Qian¹  Xu, Bing¹ 

[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

关键词: Generalized quasi-arithmetic mean;    Geometric mean;    Invariance equation;    Differential equation;   

DOI  :  10.1016/j.jmaa.2010.12.025

来源: Elsevier

【 摘 要 】

In this paper, we study the invariance of the geometric mean with respect to some generalized quasi-arithmetic means, namely, we present some results concerning the functional equation phi(-1)(integral(1)(0)phi(tx + (1 - t)y)d mu(t)) .psi(-1)(integral(1)(0)psi(tx + (1 - t)y) dv(t)) = xy, x, y is an element of I, where I is an open real interval, phi, psi : I -> R are continuous strictly monotonic unknown functions and mu, v are Borel probability measures on the interval [0,1]. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free