On Several New Hilbert-type Inequalities Involving Means Operators

被引：1
|
作者：
Vandanjav ADIYASUREN [1 ]
Tserendorj BATBOLD [2 ]
Mario KRNI [3 ]
机构：
[1] Department of Mathematical Analysis,National University of Mongolia
[2] Institute of Mathematics,National University of Mongolia
[3] Faculty of Electrical Engineering and Computing,University of
来源：
ActaMathematicaSinica | 2013年 / 29卷 / 08期
关键词：
D O I：
暂无
中图分类号：
O178 [不等式及其他];
学科分类号：
摘要：
In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.
引用
收藏
页码：1493 / 1514
页数：22
相关论文
共 50 条
  • [41] Multidimensional Hilbert-Type Inequalities with a Homogeneous Kernel
    Predrag Vuković
    Journal of Inequalities and Applications, 2009
  • [42] The refinements of Hilbert-type inequalities in discrete case
    Vukovic, Predrag
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2018, 45 (02): : 323 - 328
  • [43] On a new Hilbert-type integral inequality involving the upper limit functions
    Hongmin Mo
    Bicheng Yang
    Journal of Inequalities and Applications, 2020
  • [44] On Some New Dynamic Hilbert-Type Inequalities across Time Scales
    Zakarya, Mohammed
    Saied, Ahmed I.
    Al-Thaqfan, Amirah Ayidh, I
    Ali, Maha
    Rezk, Haytham M.
    AXIOMS, 2024, 13 (07)
  • [45] Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales
    Rezk, Haytham M.
    AlNemer, Ghada
    Saied, Ahmed, I
    Bazighifan, Omar
    Zakarya, Mohammed
    SYMMETRY-BASEL, 2022, 14 (04):
  • [46] Hilbert-Type Operators Acting on Bergman Spaces
    Aguilar-Hernandez, Tanausu
    Galanopoulos, Petros
    Girela, Daniel
    COMPUTATIONAL METHODS AND FUNCTION THEORY, 2024,
  • [47] On a new Hilbert-type integral inequality involving the upper limit functions
    Mo, Hongmin
    Yang, Bicheng
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
  • [48] A new Hilbert-type inequality
    Yang, Bicheng
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2006, 13 (03) : 479 - 487
  • [49] On the way of weight coefficient and research for the Hilbert-type inequalities
    Yang, BC
    Rassias, TM
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2003, 6 (04): : 625 - 658
  • [50] More Accurate Hilbert-Type Inequalities in a Difference Form
    Tserendorj Batbold
    Mario Krnić
    Josip Pečarić
    Results in Mathematics, 2018, 73
12345