OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS

被引：0

作者：

Long, Bo-Yong ^{[1
]}

Chu, Yu-Ming ^{[2
]}

机构：

[1] Anhui Univ, Coll Math Sci, Hefei 230039, Peoples R China

[2] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China

来源：

JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY | 2011年 / 17卷 / 02期

关键词：

Generalized logarithmic mean; arithmetic mean; harmonic mean;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we answer the question: for alpha is an element of (0,1), what are the greatest value p = p (alpha) and least value q = q (alpha), such that the double inequality L-p(a, b) <= A(alpha)(a, b)H1-alpha(a, b) <= L-q (a, b) holds for all a, b > 0? where L-p (a, b), A(a, b), and H(a, b) are the p-th generalized logarithmic, arithmetic, and harmonic means of a and b, respectively.

引用

下载

页码：85 / 96

页数：12

共 50 条

[1] Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
Qing Ding
Tiehong Zhao
Journal of Inequalities and Applications, 2017
[2] Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
Ding, Qing
Zhao, Tiehong
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[3] Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means
Qian, Wei-Mao
Long, Bo-Yong
JOURNAL OF APPLIED MATHEMATICS, 2012,
[4] OPTIMAL BOUNDS FOR THE SANDOR MEAN IN TERMS OF THE COMBINATION OF GEOMETRIC AND ARITHMETIC MEANS
Qian, Wei-Mao
Ma, Chun-Lin
Xu, Hui-Zuo
JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (02): : 667 - 674
[5] OPTIMAL CONVEX COMBINATION BOUNDS OF SEIFFERT AND GEOMETRIC MEANS FOR THE ARITHMETIC MEAN
Chu, Yu-Ming
Zong, Cheng
Wang, Gen-Di
JOURNAL OF MATHEMATICAL INEQUALITIES, 2011, 5 (03): : 429 - 434
[6] Bounds for the Convex Combination of Contra-harmonic and Harmonic Means by the Generalized Logarithmic Mean
Sonubon, Annop
Orankitjaroen, Somsak
Nonlaopon, Kamsing
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (03): : 1120 - 1143
[7] Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means
Long, Bo-Yong
Chu, Yu-Ming
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,
[8] Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means
Bo-Yong Long
Yu-Ming Chu
Journal of Inequalities and Applications, 2010
[9] OPTIMAL ONE-PARAMETER MEAN BOUNDS FOR THE CONVEX COMBINATION OF ARITHMETIC AND LOGARITHMIC MEANS
He, Zai-Yin
Wang, Miao-Kun
Chu, Yu-Ming
JOURNAL OF MATHEMATICAL INEQUALITIES, 2015, 9 (03): : 699 - 707
[10] THE OPTIMAL CONVEX COMBINATION BOUNDS OF ARITHMETIC AND HARMONIC MEANS IN TERMS OF POWER MEAN
Xia, We-Feng
Janous, Walther
Chu, Yu-Ming
JOURNAL OF MATHEMATICAL INEQUALITIES, 2012, 6 (02): : 241 - 248

← 1 2 3 4 5 →