IMPROVED JENSEN-TYPE INEQUALITIES VIA LINEAR INTERPOLATION AND APPLICATIONS

被引：20

作者：

Choi, Daeshik ^{[1
]}

Krnic, Mario ^{[2
]}

Pecaric, Josip ^{[3
]}

机构：

[1] Southern Illinois Univ, Dept Math & Stat, Box 1653, Edwardsville, IL 62026 USA

[2] Univ Zagreb, Fac Elect Engn & Comp, Unska 3, Zagreb 10000, Croatia

[3] Univ Zagreb, Fac Text Technol, Prilaz Baruna Filipovica 28a, Zagreb 10000, Croatia

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2017年 / 11卷 / 02期

关键词：

Convex function; Jensen inequality; Young inequality; Kantorovich constant; Specht ratio; arithmetic mean; geometric mean; Heinz mean; OPERATOR INEQUALITIES; HEINZ INEQUALITIES; IMPROVED YOUNG;

D O I：

10.7153/jmi-11-27

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence, we obtain improvements of some recently established Young-type inequalities. Finally, our method is also applied to matrix case. In such a way we obtain improvements of some important matrix inequalities known from the literature.

引用

页码：301 / 322

页数：22

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