Mappings related to Jensen’s and Levinson’s operator inequalities

The goal of my talk is to present some results about mappings related to Jensen's and Levinson's operator inequalities for Hilbert space operators. Some properties of these mappings are observed: operator convexity, monotonicity and quasi linearity. As applications, refinements and extensions of some know inequalities are obtained. As a continuation of this research, some inequalities of Jensen's and Levinson's type for Lipschitzian mappings between two Banach spaces are considered.