Bounds for the Combinations of Neuman-Sandor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean

被引：10
|
作者：
He, Zai-Yin [1 ]
Qian, Wei-Mao [2 ]
Jiang, Yun-Liang [3 ]
Song, Ying-Qing [4 ]
Chu, Yu-Ming [4 ]
机构：
[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China
[2] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China
[3] Huzhou Teachers Coll, Sch Informat & Engn, Huzhou 313000, Peoples R China
[4] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
关键词：
SHARP BOUNDS;
D O I：
10.1155/2013/903982
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give the greatest values r(1),r(2) and the least values s(1),s(2) in (1/2,1) such that the double inequalities C(r(1)a+(1-r(1))b,r(1)b+(1-r(1))a) < alpha A(a,b) + (1-alpha)T(a,b) < C(s(1)a + (1-s(1))b,s(1)b +(1-s(1))a) and C(r(2)a + (1-r(2))a) < alpha A(a,b) + (1-alpha)M(a,b) < C(s(2)a + (1-s(2))b,s(2)b + (1-s(2))a) hold for any alpha epsilon (0,1) and all a,b > 0 with a not equal b, where A(a,b), M(a,b), C(a,b), and T(a,b) are the arithmetic, Neuman-Sandor, contraharmonic, and second Seiffert means of a and b, respectively.
引用
收藏
页数：5
相关论文
共 50 条
  • [1] 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
  • [2] Optimal Bounds for Neuman-Sandor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means
    Zhao, Tie-Hong
    Chu, Yu-Ming
    Liu, Bao-Yu
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [3] 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,
  • [4] 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
  • [5] 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,
  • [6] Bounds for the Arithmetic Mean in Terms of the Neuman-Sandor and Other Bivariate Means
    Zhang, Fan
    Chu, Yu-Ming
    Qian, Wei-Mao
    [J]. JOURNAL OF APPLIED MATHEMATICS, 2013,
  • [7] 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,
  • [8] Bounds for the Neuman-Sandor Mean in Terms of the Arithmetic and Contra-Harmonic Means
    Li, Wen-Hui
    Miao, Peng
    Guo, Bai-Ni
    [J]. AXIOMS, 2022, 11 (05)
  • [9] SHARP BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS
    Chu, Yuming
    Zhao, Tiehong
    Song, Yingqing
    [J]. ACTA MATHEMATICA SCIENTIA, 2014, 34 (03) : 797 - 806
  • [10] 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
12345