Some Refinements and Reverses about the Hermite-Hadamard Inequalities for Pointwise Convex Maps involving Functional Arguments

Abstract

The purpose of this paper is to investigate some refinements and reverses for the Hermite-Hadamard inequalities when the integrand map is convex in functional variables with respect to the pointwise order. Our theoretical results obtained here immediately imply those of operator versions without referring to the techniques of the operator theory.