On some new converses of the Jensen and the Lah-Ribarič operator inequality

Abstract

In this paper we study some new converses of the Jensen and the LahRibarič operator inequality regarding convex functions. First we give two series of converses in a general setting. The general results are then applied to quasi-arithmetic operator means with a particular emphasis to power operator means. The obtained results are also compared with some related results, known from the literature.