On new refinement of the Jensen inequality using uniformly convex functions with applications

Abstract

One of the fundamental inequalities which is used in many inequities is Jensen inequality. In fact, it is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies and information theory. The purpose of this research paper is to give a new interesting refinement of Jensen inequality for two particular finite sequences by using uniformly convex function. Also, we give some applications of this in information theory.

Keywords:

• Jensen's inequality
• means
• csiszár divergence
• global bounds
• Shannon entropy
• uniformly convex function

Mathematics subject classification (2010):

• 94A17
• 26D20
• 26D15
• 26D10

Disclosure statement

No potential conflict of interest was reported by the authors.