Mustapha Raïssouli, Rabie Zine. Source: Annals of Functional Analysis, Volume 10, Number 3, 357--369.Abstract:
In this paper, we give some refinements and reverses for the Hermite–Hadamard inequality when the integrand map is the Fenchel conjugate in convex analysis. The theoretical results obtained by our present functional approach immediately imply those of an operator version in a simple and elegant way. An application for scalar means is provided as well.