Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 45 – 56
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0134
On Schur power convexity of generalized invariant contra harmonic means with respect to geometric means
Huan-Nan Shi\(^{1}\), Fei Wang\(^{2}\), Jing Zhang\(^{3}\) and Wei-Shih Du\(^{4,*}\)
\(^{1}\) Department of Electronic Information, Teacher’s College, Beijing Union University, Beijing City, 100011, China
\(^{2}\) Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou, Zhejiang, 310053, China
\(^{3}\) Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China
\(^{4}\) Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Copyright © 2024 Huan-Nan Shi, Fei Wang, Jing Zhang and 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: April 30, 2024 – Accepted: June 28, 2024 – Published: June 30, 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.