Double precision of the Jensen-type operator inequalities for bounded and Lipschitzian functions

摘要

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