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Schur power convexity of Gini means

Zhen-Hang Yang
대한수학회 (The Korean Mathematical Society)|2013.03|대한수학회보 (Bulletin of the KMS)|제50권 제2호|pp. 485-498

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참고문헌

키워드

Schur convexitySchur power convexityGini means
주제분류수학

초록

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 : R+ → R is defined as f(x) = (xm −1)/m if m 6≠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.

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 : R+ → R is defined as f(x) = (xm −1)/m if m 6≠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.

참고문헌 (50)

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