NECESSARY AND SUFFICIENT CONDITIONS FOR THE SCHUR HARMONIC CONVEXITY OR CONCAVITY OF THE EXTENDED MEAN VALUES

被引：0

作者：

Xia, Wei-Feng ^{[2
]}

Chu, Yu-Ming ^{[1
]}

Wang, Gen-Di ^{[1
]}

机构：

[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China

[2] Huzhou Teachers Coll, Sch Teacher Educ, Huzhou 313000, Peoples R China

来源：

REVISTA DE LA UNION MATEMATICA ARGENTINA | 2011年 / 52卷 / 01期

关键词：

extended mean value; Schur-convex; Schur harmonic convex; HEISENBERG-GROUP; INEQUALITIES; MANIFOLDS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that the extended values E(r, s; x, y) are Schur harmonic convex (or concave, respectively) with respect to (x, y) is an element of (0, infinity) x (0, infinity) if and only if (r, s) is an element of {(r, s) : s >= 1,s >= r, s + r + 3 >= 0} boolean OR {(r, s) : r >= -1, r >= s, s + r + 3 >= 0} (or {(r, s) : s <= -1, r <= -1, s + r + 3 <= 0}, respectively).

引用

页码：121 / 132

页数：12

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