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

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.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.