A positive answer to Bhatia-Li conjecture on the monotonicity for a new mean in its parameter

被引：23

作者：

Yang, Zhen-Hang ^{[1
,2
]}

Tian, Jing-Feng ^{[3
,4
]}

Wang, Miao-Kun ^{[5
]}

机构：

[1] North China Elect Power Univ, Engn Res Ctr Intelligent Comp Complex Energy Syst, Minist Educ, Yonghua St 619, Baoding 071003, Peoples R China

[2] Zhejiang Soc Elect Power, Hangzhou 310014, Zhejiang, Peoples R China

[3] Hebei Univ, Sch Management, Wusi Rd 180, Baoding 071002, Peoples R China

[4] North China Elect Power Univ, Dept Math & Phys, Yonghua St 619, Baoding 071003, Peoples R China

[5] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2020年 / 114卷 / 03期

关键词：

R-function; Hypergeometric series; Gamma function; Beta function; INEQUALITIES;

D O I：

10.1007/s13398-020-00856-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Bhatia-Li mean B-p (x, y) of positive numbers x and y is defined as where B (center dot, center dot) is the Beta function. This new family of means includes the famous logarithmic mean, the Gaussian arithmetic-geometric mean etc. In 2012, Bhatia and Li conjectured that Bp ( x, y) is an increasing function of the parameter p on [0,8]. In this paper, we give a positive answer to this conjecture. Moreover, the mean Bp (x, y) is generalized to an multivariate mean and its elementary properties are investigated.

引用

页数：22

共 20 条

[1]

[Anonymous], 1975, Mathematics Magazine

[2]

[Anonymous], 1999, Encyclopedia of Mathematics and its Applications

[3] Inequalities for the gamma function [J].

Batir, Necdet .

ARCHIV DER MATHEMATIK, 2008, 91 (06) :554-563

[4]

Bhatia R., 2012, Commun. Stoch. Anal., V6, P15

[5]

BORWEIN J. M., 1987, Pi and the AGM

[6]

Carlson B. C., 1963, J. Math. Anal. Appl., V7, P452

[7] A HYPERGEOMETRIC MEAN VALUE [J].

CARLSON, BC .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (04) :759-&

[8] SOME INEQUALITIES FOR HYPERGEOMETRIC FUNCTIONS [J].

CARLSON, BC .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 17 (01) :32-&

[9]

Carlson BC., 1977, Special functions of applied mathematics

[10]

Stegun I. A., 1972, Applied Mathematics Series, V55

← 1 2 →