Demonstration of the strength of strong convexity via Jensen's gap

Year 2023, Volume: 72 Issue: 4, 1019 - 1033, 29.12.2023

Asia K Shahid Khan

https://doi.org/10.31801/cfsuasmas.1186649

Abstract

This paper demonstrates through a numerical experiment that utilization of strongly convex functions strengthens the bound presented for the Jensen gap in [4]. Consequently the improved result enables to present improvements in the bounds obtained for the Hölder and Hermite-Hadamard gaps and proposes such improvements in the results obtained for various entropies and divergences in information theory.

Keywords

Jensen inequality, strong convex function, Hölder inequality, Hermite-Hadamard ineguality, Taylor formula

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