Ela Refinements of the Operator Jensen – Mercer Inequality

Abstract

A Hermite–Hadamard–Mercer type inequality is presented and then generalized to Hilbert space operators. It is shown that f ( M +m− ∑ n i=1 xiAi ) ≤ f(M) + f(m)− ∑ n i=1 f(xi)Ai, where f is a convex function on an interval [m,M ] containing 0, xi ∈ [m,M ], i = 1, . . . , n, and Ai are positive operators acting on a finite dimensional Hilbert space whose sum… (More)

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