On the Operator Jensen-Mercer Inequality
Functional Analysis
2020-03-06 v4
Abstract
Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without assuming convexity nor operator convexity. Yet, this form refines the known inequalities in the literature. Second, we present a log-convex version for operators. We then use these results to refine some inequalities related to quasi-arithmetic means of Mercer's type for operators.
Cite
@article{arxiv.1709.01808,
title = {On the Operator Jensen-Mercer Inequality},
author = {H. R. Moradi and S. Furuichi and M. Sababheh},
journal= {arXiv preprint arXiv:1709.01808},
year = {2020}
}