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
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