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=8 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 article, we use s-convex and Green functions to obtain a bound for the Jensen gap in discrete form and a bound for the Jensen gap in integral form. We present two numerical examples to verify the main results and to examine the tightness of the bounds. Then, as an application of the discrete result, we derive a converse of the Hölder inequality. Based on the integral result, we obtain a bound for the Hermite-Hadamard gap and present a converse of the Hölder inequality in its integral form. Also, we obtain bounds for the Csiszár and Rényi divergences as applications of the discrete result. Finally, we utilize the bound obtained for the Csiszár divergence to deduce new estimates for some other divergences in information theory.