• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.485-498
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• 2013

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.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.503-520
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• 2023

In this paper, using the theory of majorization, we discuss the Schur m power convexity for L-conjugate means of n variables and the Schur convexity for weighted L-conjugate means of n variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about n variables Gini mean are established.