Reverses and Refinements of Jensen's Inequality for Positive Linear Functionals on Hermitian Unital Banach *-Algebras

Abstract

We establish in this paper some inequalities for analytic and convex functions on an open interval and positive normalized functionals defined on a Hermitian unital Banach *-algebra. Reverses and refinements of Jensen's and Slater's type inequalities are provided. Some examples for particular convex functions of interest are given as well.