New Estimates for the Jensen Gap Using s-Convexity With Applications - Adil Khan, Muhammad; Khan, Shahid; Chu, Yu-Ming (Frontiers in Physics, 2020)
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.