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J. Korean Math. Soc. 2023; 60(3): 503-520

Online first article April 24, 2023      Printed May 1, 2023

https://doi.org/10.4134/JKMS.j220039

Copyright © The Korean Mathematical Society.

Schur convexity of $L$-conjugate means and its applications

Chun-Ru Fu , Huan-Nan Shi, Dong-Sheng Wang

Beijing Union University; Beijing Union University; Beijing Polytechnic

Abstract

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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.

Keywords: $L$-conjugate means, weighted $L$-conjugate means, Schur convexity, Schur $m$ power convexty, majorization

MSC numbers: Primary 26E60, 26D15, 26B25

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