Mustapha Raïssouli. Source: Annals of Functional Analysis, Volume 10, Number 2, 252--261.Abstract:
Our main goal in this article is to give some functional inequalities involving a (convex) functional and its Fenchel conjugate. As a consequence, we obtain some refinements of the so-called Fenchel inequality as well as its reverse. Inequalities of interest illustrating the previous theoretical results are provided as well.