Optimal bounds for the Neuman-Sandor mean in terms of the first Seiffert and quadratic means

被引：2
作者：
Gong, Wei-Ming [1 ]
Shen, Xu-Hui [2 ]
Chu, Yu-Ming [1 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
[2] Huzhou Teachers Coll, Coll Nursing, Huzhou 313000, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年
关键词：
Neuman-Sandor mean; first Seiffert mean; quadratic mean; SHARP BOUNDS; INEQUALITIES;
D O I：
10.1186/1029-242X-2013-552
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we find the least value a and the greatest value beta such that the double inequality P-alpha(a, b)Q(1-alpha)(a, b) < M(a, b) < P-beta(a, b)Q(1-beta)(a, b) holds true for all a, b > 0 with a not equal b, where P(a, b), M(a, b) and Q(a, b) are the first Seiffert, Neuman-Sandor and quadratic means of a and b, respectively.
引用
收藏
页数：13
相关论文
共 18 条
  • [1] [Anonymous], J MATH SCI ADV APPL
  • [2] [Anonymous], 2002, J. Inequal. Pure Appl. Math
  • [3] [Anonymous], 2003, INT J MATH MATH SCI
  • [4] Chu Y-M, ARXIV12092920V1MATHC
  • [5] Chu YM, 2012, MATH INEQUAL APPL, V15, P415
  • [6] Sharp bounds for Seiffert mean in terms of root mean square
    Chu, Yu-Ming
    Hou, Shou-Wei
    Shen, Zhong-Hua
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012, : 1 - 6
  • [7] Optimal combinations bounds of root-square and arithmetic means for Toader mean
    Chu, Yu-Ming
    Wang, Miao-Kun
    Qiu, Song-Liang
    [J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2012, 122 (01): : 41 - 51
  • [8] A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means
    Gong, Wei-Ming
    Song, Ying-Qing
    Wang, Miao-Kun
    Chu, Yu-Ming
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [9] Optimal inequalities between Seiffert's mean and power means
    Hästö, PA
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2004, 7 (01): : 47 - 53
  • [10] Jiang W., PREPRINT
12