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http://dx.doi.org/10.4134/BKMS.2013.50.2.485

SCHUR POWER CONVEXITY OF GINI MEANS  

Yang, Zhen-Hang (System Division Zhejiang Province Electric Power Test and Research Institute)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 485-498 More about this Journal
Abstract
In this paper, the Schur convexity is generalized to Schur $f$-convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When $f$ : ${\mathbb{R}}_+{\rightarrow}{\mathbb{R}}$ is defined as $f(x)=(x^m-1)/m$ if $m{\neq}0$ and $f(x)$ = ln $x$ if $m=0$, the necessary and sufficient conditions for $f$-convexity (is called Schur $m$-power convexity) of Gini means are given, which generalize and unify certain known results.
Keywords
Schur convexity; Schur power convexity; Gini means;
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