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).

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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

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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. https://doi.org/10.68381/jca15048

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.