Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications

被引：22
作者：
Adiyasuren, Vandanjav [1 ]
Batbold, Tserendorj [2 ]
Krnic, Mario [3 ]
机构：
[1] Natl Univ Mongolia, Dept Math Anal, Ulaanbaatar 14201, Mongolia
[2] Natl Univ Mongolia, Inst Math, Ulaanbaatar 14201, Mongolia
[3] Univ Zagreb, Fac Elect Engn & Comp, Zagreb 10000, Croatia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 231卷
关键词：
Half-discrete Hilbert-type inequality; Hardy inequality; Carleman inequality; Knopp inequality; The best constant; Arithmetic mean; Geometric mean; Harmonic mean;
D O I：
10.1016/j.amc.2014.01.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we derive several new half-discrete Hilbert-type inequalities with a general homogeneous kernel, involving arithmetic, geometric and harmonic mean operators. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：148 / 159
页数：12
相关论文
共 35 条
  • [1] Half-discrete Hilbert-type inequalities involving differential operators
    Vandanjav Adiyasuren
    Tserendorj Batbold
    Mario Krnić
    Journal of Inequalities and Applications, 2014
  • [2] Half-discrete Hilbert-type inequalities involving differential operators
    Adiyasuren, Vandanjav
    Batbold, Tserendorj
    Krnic, Mario
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [3] HILBERT-TYPE INEQUALITIES INVOLVING DIFFERENTIAL OPERATORS, THE BEST CONSTANTS, AND APPLICATIONS
    Adiyasuren, Vandanjav
    Batbold, Tserendorj
    Krnic, Mario
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2015, 18 (01): : 111 - 124
  • [4] A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel
    Krnic, Mario
    Pecaric, Josip
    Vukovic, Predrag
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2013, 10 (04) : 1697 - 1716
  • [5] A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel
    Mario Krnić
    Josip Pečarić
    Predrag Vuković
    Mediterranean Journal of Mathematics, 2013, 10 : 1697 - 1716
  • [6] A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE
    Yang, Bicheng
    He, Bing
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (03): : 977 - 991
  • [7] A more accurate half-discrete Hilbert-type inequality in the whole plane and the reverses
    Rassias, Michael Th
    Yang, Bicheng
    Meletiou, Gerasimos C.
    ANNALS OF FUNCTIONAL ANALYSIS, 2021, 12 (03)
  • [8] A more accurate half-discrete Hilbert-type inequality in the whole plane and the reverses
    Michael Th. Rassias
    Bicheng Yang
    Gerasimos C. Meletiou
    Annals of Functional Analysis, 2021, 12
  • [9] On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function
    Rassias, M.T. (michail.rassias@math.ethz.ch), 1600, Elsevier Inc. (242): : 800 - 813
  • [10] HILBERT-TYPE INEQUALITIES FOR HILBERT SPACE OPERATORS
    Krnic, Mario
    QUAESTIONES MATHEMATICAE, 2013, 36 (02) : 209 - 223
1234