Refinements of Hermite-Hadamard type inequalities for operator convex functions

Abstract

The purpose of this paper is to present some new versions of Hermite-Hadamard type inequalities for operator convex functions. We give refinements of Hermite-Hadamard type inequalities for convex functions of self-adjoint operators in a Hilbert space analogous to well-known inequalities of the same type. The results presented in this paper are more general than known results given by several authors. MSC: 26D15; 47A63

New refinements of the Hermite–Hadamard inequalities based on ψ-Hilfer fractional integrals

“…H-HI with the help of fractional integrals in the literature. For instance, the authors in [3] consider H-HI (1.1) as the form…”

Some Hermite-Hadamard type inequalities for operator convex functions and positive maps

“…For recent related results on operator Hermite-Hadamard type inequalities, see [1]- [2], [5]- [10] and [13]. Let H be a complex Hilbert space and B (H) , the Banach algebra of bounded linear operators acting on H. We denote by B + (H) the convex cone of all positive operators on H and by B ++ (H) the convex cone of all positive de nite operators on H.…”

Refinements of Hermite-Hadamard inequality for operator convex function

“…For recent related results on Hermite-Hadamard type operator inequality, see [1,8,11]. In this paper, we present several operator versions of the Hermite-Hadamard inequality for the operator convex function, which are refinements of operator convex inequalities (1.2) and (1.3).…”