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

被引：4

作者：

Zhang, Qian ^{[1
]}

Xu, Bing ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 379卷 / 01期

关键词：

Generalized quasi-arithmetic mean; Geometric mean; Invariance equation; Differential equation;

D O I：

10.1016/j.jmaa.2010.12.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：65 / 74

页数：10

共 50 条

[1] The invariance of the arithmetic mean with respect to generalized quasi-arithmetic means
Mako, Zita
Pales, Zsolt
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 353 (01) : 8 - 23
[2] Invariance of a quasi-arithmetic mean with respect to a system of generalized Bajraktarevic means
Matkowski, Janusz
[J]. APPLIED MATHEMATICS LETTERS, 2012, 25 (11) : 1651 - 1655
[3] Invariance equation for generalized quasi-arithmetic means
Szabolcs Baják
Zsolt Páles
[J]. Aequationes mathematicae, 2009, 77 : 133 - 145
[4] Invariance equation for generalized quasi-arithmetic means
Bajak, Szabolcs
Pales, Zsolt
[J]. AEQUATIONES MATHEMATICAE, 2009, 77 (1-2) : 133 - 145
[5] Invariance of Bajraktarevic mean with respect to quasi arithmetic means
Matkowski, Janusz
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2012, 80 (3-4): : 441 - 455
[6] On the invariance of the arithmetic mean with respect to generalized Bajraktarević means
R. Grünwald
Zs. Páles
[J]. Acta Mathematica Hungarica, 2022, 166 : 594 - 613
[7] ON THE INVARIANCE OF THE ARITHMETIC MEAN WITH RESPECT TO GENERALIZED BAJRAKTAREVIC MEANS
Grunwald, R.
Pales, Zs
[J]. ACTA MATHEMATICA HUNGARICA, 2022, 166 (02) : 594 - 613
[8] Characterization of generalized quasi-arithmetic means
Matkowski J.
Pales Z.
[J]. Acta Scientiarum Mathematicarum, 2015, 81 (3-4): : 447 - 456
[9] Invariance of quasi-arithmetic means with function weights
Jarczyk, Justyna
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 353 (01) : 134 - 140
[10] On the equality of generalized quasi-arithmetic means
Mako, Zita
Pales, Zsolt
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2008, 72 (3-4): : 407 - 440

← 1 2 3 4 5 →