Journal of Convex Analysis 15 (2008), No. 4, 707--718
Copyright Heldermann Verlag 2008
The Schur Geometrical Convexity of the Extended Mean Values
Yuming Chu
Dept. of Mathematics, Huzhou Teachers College, Zhejiang, Huzhou 313000, P. R. China
chuyuming@hutc.zj.cn
Xiaoming Zhang
Haining Radio and TV University, Haining 314400, P. R. China
Gendi Wang
Dept. of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China
[Abstract-pdf]
We prove that the extended mean values $E(r,s;x,y)$ are Schur geometrically convex (or concave, respectively) with respect to $(x,y)\in(0,\infty)\times(0,\infty)$ if and only if $s+r\geq 0$ (or $s+r\leq 0$,respectively).
Keywords: Extended mean value, Schur convex, Schur concave, Schur geometrically convex, Schur geometrically concave.
MSC: 26B25
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