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).
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页码：121 / 132
页数：12
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