SHARP BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

被引：50
|
作者：
Chu, Yuming [1 ]
Zhao, Tiehong [2 ]
Song, Yingqing [1 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 03期
关键词：
Neuman-Sandor mean; quadratic mean; first Seiffert mean; INEQUALITIES;
D O I：
10.1016/S0252-9602(14)60050-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we prove that the double inequality alpha P(a, b) + (1-alpha)Q(a, b) < M (a,b) < beta P(a, b) + (1-beta)Q (a,b) holds for any a, b > 0 with a not equal b if and only if alpha > 1/2 and beta <= [pi root 2(log(1 + root 2 -1)] /[root 2 pi-2) log(1 + root 2)] = 0.359..., where M(a, b), Q(a, b), and P(a, b) are the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively.
引用
收藏
页码：797 / 806
页数：10
相关论文
共 50 条
  • [1] Optimal bounds for the Neuman-Sandor mean in terms of the first Seiffert and quadratic means
    Gong, Wei-Ming
    Shen, Xu-Hui
    Chu, Yu-Ming
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [2] Optimal Bounds for the Neuman-Sandor Mean in terms of the Convex Combination of the First and Second Seiffert Means
    Cui, Hao-Chuan
    Wang, Nan
    Long, Bo-Yong
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
  • [3] OPTIMAL BOUNDS FOR THE FIRST SEIFFERT MEAN IN TERMS OF THE CONVEX COMBINATION OF THE LOGARITHMIC AND NEUMAN-SANDOR MEAN
    Lei, Jian-Jun
    Chen, Jing-Jing
    Long, Bo-Yong
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2018, 12 (02): : 365 - 377
  • [4] Optimal bounds for Neuman-Sandor mean in terms of the convex combination of the logarithmic and the second Seiffert means
    Chen, Jing-Jing
    Lei, Jian-Jun
    Long, Bo-Yong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [5] Optimal bounds for Neuman-Sandor mean in terms of the geometric convex combination of two Seiffert means
    Huang, Hua-Ying
    Wang, Nan
    Long, Bo-Yong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 11
  • [6] Sharp bounds for Seiffert and Neuman-Sandor means in terms of generalized logarithmic means
    Chu, Yu-Ming
    Long, Bo-Yong
    Gong, Wei-Ming
    Song, Ying-Qing
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [7] SHARP BOUNDS FOR NEUMAN-SNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS
    褚玉明
    赵铁洪
    宋迎清
    [J]. Acta Mathematica Scientia, 2014, 34 (03) : 797 - 806
  • [8] Sharp bounds for the Neuman-Sandor mean in terms of the power and contraharmonic means
    Jiang, Wei-Dong
    Qi, Feng
    [J]. COGENT MATHEMATICS, 2015, 2
  • [9] OPTIMAL BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF LOGARITHMIC AND QUADRATIC OR CONTRA-HARMONIC MEANS
    Chu, Yuming
    Zhao, Tiehong
    Liu, Baoyu
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2014, 8 (02): : 201 - 217
  • [10] Bounds for the Combinations of Neuman-Sandor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean
    He, Zai-Yin
    Qian, Wei-Mao
    Jiang, Yun-Liang
    Song, Ying-Qing
    Chu, Yu-Ming
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2013,
12345