New refinement of the Jensen inequality associated to certain functions with applications

Abstract

Abstract This article proposes a new refinement of the celebrated Jensen inequality. Some refinements have been obtained for quasi-arithmetic means, Hölder and Hermite–Hadamard inequalities. Several applications are given in information theory. A more general refinement of Jensen inequality is presented associated to n functions.

Keywords

• Jensen’s inequality
• Convex functions
• Hölder inequality
• Means
• Csiszár divergence
• Shannon entropy