OPTIMAL BOUNDS FOR TOADER MEAN IN TERMS OF QUADRATIC, CONTRA-HARMONIC AND SECOND NEUMAN MEANS

被引：0
|
作者：
Yang, Yue-Ying [1 ]
Qian, Wei-Mao [2 ]
Chu, Yu-Ming [3 ]
机构：
[1] Huzhou Vocat & Tech Coll, Sch Mech & Elect Engn, Huzhou 313000, Peoples R China
[2] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China
[3] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS | 2018年 / 9卷 / 04期
关键词：
Toader mean; Neuman mean; quadratic mean; contra-harmonic mean; complete elliptic integral;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the article, we prove that the double inequalities alpha N-AG(a, b) + (1 - alpha)Q(a, b) < TD (a, b) < beta N-AG(a, b) + (1 - beta)Q(a, b), lambda N-AG(a, b) + (1 - lambda)C(a, b) < TD (a, b) < mu N-AG(a, b) + (1 - mu)C(a, b) hold for all a, b > 0 with a not equal b if and only if alpha >= 3/10, beta <= 2 (root 2 pi - 4) / [(2 root 2 - 1)pi] = 0.1542 ..., lambda >= 9/16 and mu <= 4 (pi - 2) / (3 pi) = 0.4845 ..., where Q (a, b), C(a, b), NAG (a, b) and TD(a, b) are the quadratic, contra-harmonic, second Neuman and Toader means of a and b, respectively.
引用
收藏
页码：28 / 38
页数：11
相关论文
共 50 条
  • [1] 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
  • [2] 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)
  • [3] Sharp bounds for Toader mean in terms of arithmetic, quadratic, and Neuman means
    Li, Jun-Feng
    Qian, Wei-Mao
    Chu, Yu-Ming
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
  • [4] Sharp bounds for Toader mean in terms of arithmetic, quadratic, and Neuman means
    Jun-Feng Li
    Wei-Mao Qian
    Yu-Ming Chu
    [J]. Journal of Inequalities and Applications, 2015
  • [5] Sharp bounds for the Neuman mean in terms of the quadratic and second Seiffert means
    Chu, Yu-Ming
    Wang, Hua
    Zhao, Tie-Hong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [6] Sharp bounds for the Neuman mean in terms of the quadratic and second Seiffert means
    Yu-Ming Chu
    Hua Wang
    Tie-Hong Zhao
    [J]. Journal of Inequalities and Applications, 2014
  • [7] Optimal bounds for Toader mean in terms of general means
    Qian Zhang
    Bing Xu
    Maoan Han
    [J]. Journal of Inequalities and Applications, 2020
  • [8] Optimal bounds for Toader mean in terms of general means
    Zhang, Qian
    Xu, Bing
    Han, Maoan
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
  • [9] Bounds for the Convex Combination of Contra-harmonic and Harmonic Means by the Generalized Logarithmic Mean
    Sonubon, Annop
    Orankitjaroen, Somsak
    Nonlaopon, Kamsing
    [J]. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (03): : 1120 - 1143
  • [10] Optimal Bounds for Neuman Means in Terms of Harmonic and Contraharmonic Means
    He, Zai-Yin
    Chu, Yu-Ming
    Wang, Miao-Kun
    [J]. JOURNAL OF APPLIED MATHEMATICS, 2013,
12345