OPTIMAL ONE-PARAMETER MEAN BOUNDS FOR THE CONVEX COMBINATION OF ARITHMETIC AND LOGARITHMIC MEANS

被引：2
|
作者：
He, Zai-Yin [1 ]
Wang, Miao-Kun [1 ]
Chu, Yu-Ming [1 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2015年 / 9卷 / 03期
关键词：
One-parameter mean; arithmetic mean; logarithmic mean; INEQUALITIES; VARIABLES;
D O I：
10.7153/jmi-09-58
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find the greatest value p(1) = p(1)(alpha) and the least value p(2) = p(2)(alpha) such that the double inequality J(p1) (a, b) < alpha A(a, b)+(1-alpha)L(a, b) < J(p2) (a, b) holds for any alpha is an element of (0,1) and all a, b > 0 with a not equal b. Here, A(a, b), L(a, b) and J(p)(a, b) denote the arithmetic, logarithmic and p-th one-parameter means of two positive numbers a and b, respectively.
引用
收藏
页码：699 / 707
页数：9
相关论文
共 50 条
  • [41] Sharp one-parameter geometric and quadratic means bounds for the Sándor–Yang means
    Bo Wang
    Chen-Lan Luo
    Shi-Hui Li
    Yu-Ming Chu
    [J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, 114
  • [42] Proof of One Optimal Inequality for Generalized Logarithmic, Arithmetic, and Geometric Means
    Ladislav Matejíčka
    [J]. Journal of Inequalities and Applications, 2010
  • [43] 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
  • [44] Proof of One Optimal Inequality for Generalized Logarithmic, Arithmetic, and Geometric Means
    Matejicka, Ladislav
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,
  • [45] 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
  • [46] Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean
    Zhu, Ling
    Malesevic, Branko
    [J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (02)
  • [47] Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean
    Ling Zhu
    Branko Malešević
    [J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117
  • [48] Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values
    Qi, Feng
    Cerone, Pietro
    Dragomir, Sever S.
    Srivastava, H. M.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 208 (01) : 129 - 133
  • [49] SHARP BOUNDS FOR SANDOR-YANG MEANS IN TERMS OF ONE-PARAMETER FAMILY OF BIVARIATE MEANS
    Yang, Yue-Ying
    Qian, Wei-Mao
    Xu, Hui-Zuo
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (04): : 1181 - 1196
  • [50] NEW SHARP BOUNDS FOR IDENTRIC MEAN IN TERMS OF LOGARITHMIC MEAN AND ARITHMETIC MEAN
    Yang, Zhen-Hang
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2012, 6 (04): : 533 - 543
12345