Convex inequalities and their applications to relative operator entropies
Classical Analysis and ODEs
2022-02-10 v1 Functional Analysis
Abstract
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex functions. As their consequences, we derive the refinements for Young's inequality and Jensen's inequality. In addition, the operator Jensen's type inequality is also developed for conditioned two functions. Utilizing these new inequalities, we investigate the operator inequalities related to the relative operator entropy.
Keywords
Cite
@article{arxiv.2202.04299,
title = {Convex inequalities and their applications to relative operator entropies},
author = {Shigeru Furuichi and Hamid Reza Moradi and Supriyo Dutta},
journal= {arXiv preprint arXiv:2202.04299},
year = {2022}
}
Comments
13 pages