Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 15 (2008), No. 4, 707--718Copyright 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 [ Fulltext-pdf  (131  KB)] for subscribers only.