New Jensen's bounds for HA-convex mappings with applications to Shannon entropy

Abstract

The aim of this article is to establish some new extensions and variants of Jensen’s discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions. We introduce uniformly HA-convex functions, which are the generalized class of HA-convex (harmonic-arithmetic)-convex functions and provide some examples too. As an application point of view for the new Jensen’s bounds, we present some new improved bounds for Shannon’s entropy. Finally, some analysis is given by graphical illustration to prove the improvements of bounds.

Keywords

• shannon’s entropy
• jensen’s inequality
• ha-convex function
• uniformly ha-convex function
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