AUTHOR=Adil Khan Muhammad , Khan Shahid , Chu Yu-Ming 

TITLE=New Estimates for the Jensen Gap Using s-Convexity With Applications

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00313

DOI=10.3389/fphy.2020.00313

ISSN=2296-424X

ABSTRACT=In this manuscript, we utilize s-and Green convex functions to obtain a bound for the Jensen gap in discrete form and a bound for the Jensen gap in integral form. As an application of the discrete result, we derive a converse of the Holder inequality. Based on the integral result, we obtain a bound for the Hermite Hadamard gap and present a converse of the Holder inequality in its integral version. Also, we present bounds for Csiszar and Renyi divergences as applications of the discrete result. Finally, we utilize the
bound obtained for Csiszar divergence, and deduce new estimates for other divergences in information theory.