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

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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