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Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (Online) 2616-8103 (Print)
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  • Research article

On Schur power convexity of generalized invariant contra harmonic means with respect to geometric means

Author(s): Huan-Nan Shi1, Fei Wang2, Jing Zhang3, Wei-Shih Du4
1Department of Electronic Information, Teacher’s College, Beijing Union University, Beijing City, 100011, China
2Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou, Zhejiang, 310053, China
3Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China
4Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Copyright © Huan-Nan Shi, Fei Wang, Jing Zhang, Wei-Shih Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 30/04/2024
  • Accepted: 28/06/2024
  • Published: 30/06/2024

Abstract

In this article, we investigate the power convexity of two generalized forms of the invariant of the contra harmonic mean with respect to the geometric mean, and establish several inequalities involving bivariate power mean as applications. Some open problems related to the Schur power convexity and concavity are also given.

Keywords: Schur power convexity; generalized invariant contra harmonic mean; majorization; binary power mean.
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