Monotonicity of ratio between the generalized logarithmic means

被引：0

作者：

Qi, Feng ^{[1
]}

Chen, Shou-Xin

Chen, Chao-Ping

机构：

[1] Henan Univ, Coll Math & Informat Sci, Kaifeng City 475001, Henan, Peoples R China

[2] Henan Polytech Univ, Res Inst Math Inequal Theory, Jiaozuo 454010, Peoples R China

[3] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Peoples R China

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2007年 / 10卷 / 03期

关键词：

monotonicity; inequality; ratio; generalized logarithmic mean; extended logarithmic mean; identric mean; exponential mean;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let c > b > a > 0 be real numbers. Then the function f (r) = L-r(a,b)/L-r(a,c) is strictly decreasing on (-infinity, infinity), where L-r (a, b) denotes the generalized (extended) logarithmic mean of two positive numbers a and b.

引用

页码：559 / 564

页数：6

共 52 条

[1] ON AN INEQUALITY OF MINC,H. AND SATHRE,L [J].

ALZER, H .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 179 (02) :396-402

[2]

Bullen, 1998, PITMAN MONOGRAPHS SU, V97

[3] On a generalization of Martins' inequality [J].

Chan, TH ;

Gao, P ;

Qi, F .

MONATSHEFTE FUR MATHEMATIK, 2003, 138 (03) :179-187

[4]

CHAN TH, 2001, RGMIA RES REP COLL, V4, P93

[5]

Chen CP, 2003, MATH INEQUAL APPL, V6, P229

[6]

CHEN CP, 2002, RGMIA RES REP COLL, V5

[7] On Alzer's inequality [J].

Elezovic, N ;

Pecaric, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (01) :366-369

[8]

Guo B.-N., 2003, TAMKANG J MATH, V34, P261

[9]

Guo BN, 2006, MATH INEQUAL APPL, V9, P1

[10]

GUO BN, 2001, RGMIA RES REP COLL, V4, P55

← 1 2 3 4 5 6 →