Some inequalities for convex functions and applications to operator inequalities

Abstract

In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.