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

In this paper we study some new converses of the Jensen and the Lah-Ribarič 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.

Jensen operator inequality; Lah-Ribarič operator inequality; convexity; operator convexity; converse

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