On parameter dependent refinement of discrete Jensen's inequality for operator convex functions

Abstract

In this paper, we consider the class of self-adjoint operators defined on a Hilbert space, whose spectra are contained in an interval. We give parameter dependent renement of the well known discrete Jensen's inequality in this class. The parameter dependent mixed symmetric means are defined for a subclass of positive self-adjoint operators which insure the refinements of inequality between power means of strictly positive operators.