Abstract

We prove that the extended mean values E(r,s;x,y)E(r,s;x,y) are Schur geometrically convex (or concave, respectively) with respect to (x,y)∈(0,∞)×(0,∞)(x,y)\in(0,\infty)\times(0,\infty) if and only if s+r≥0s+r\geq 0 (or s+r≤0s+r\leq 0,respectively).

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Extended mean value
  • Schur convex
  • Schur concave
  • Schur geometrically convex
  • Schur geometrically concave

Mathematics Subject Classification

26B25

Suggested citation

Y. Chu, X. Zhang, G. Wang. “The Schur Geometrical Convexity of the Extended Mean Values.” Journal of Convex Analysis 15 (2008), No. 4, 707–718.

Copyright Heldermann Verlag 2008