engleski

Jensen-type operator inequalities for bounded, Lipschitzian and higher order convex functions

The main objective of this talk is a study of mutual bounds for the Jensen operator inequality and the Lah-Ribariˇc operator inequality for the classes of bounded, Lipschitzian and higher order convex functions. The connection with the classical convexity is also discussed. As an application, our main results are then applied to quasi-arithmetic operator means, with a particular emphasis to power operator means. In particular, we obtain some new reverse relations that correspond to quasi-arithmetic and power operator means.

Jensen operator inequality, Lah-Ribariˇc operator inequality, convexity, operator convexity, bounded function, Lipschitzian function

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