
Journal of Convex Analysis 15 (2008), No. 4, 707718 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 [Abstractpdf] 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 [ Fulltextpdf (131 KB)] for subscribers only. 