Strong Estimations of Information Inequalities

Abstract

We explore a specific subclass of convex functions that exhibit enhanced and superior char- acteristics, known as strong convex functions. By focusing on strong convexity, we revisit classical inequalities like Jensen’s and Hermite-Hadamard (HH) type inequalities. This ap- proach leads to more robust estimates and refinements of well-known divergence measures such as Kullback-Liebler (KL), χ2- and Jeffreys divergence, among others. Moreover, we extend our investigations to improving Riemann-Liouville HH ϒ-divergence inequal- ities specifically designed for strongly convex functions. These improvements serve as a foundation to bridge fractional information inequalities with recent significant research outcomes, providing valuable insights and connections within the field of mathematical analysis and information theory. We explore various novel bounds for Csiszar and related divergences and for Zipf-Mandelbrot entropy by means of Jensen-Mercer’s inequality via strongly convex function.