Refinements of the operator Jensen-Mercer inequality

By M. Kian, Mohammad Sal Moslehian. 2013

108 citations recorded by the source corpus.

A Hermite-Hadamard-Mercer type inequality is presented and then generalized to Hilbert space operators. It is shown that f M + m Pn=1 xiAi � � f(M)+f(m) Pn=1 f(xi)Ai, where f is a convex function on an interval (m,M) containing 0, xi 2 (m,M), i = 1,...,n, and Ai are positive operators acting on a finite dimensional Hilbert space whose sum is equal to the identity operator. A Jensen-Mercer operator type inequality for separately operator convex functions is also presented.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b1f6a6dd397cb2e275f4f3674809a97942e083d7