Refinements Jensen's Inequality and Some Their Applications

Year 2024, Volume: 12 Issue: 2, 112 - 119, 28.10.2024

Mehmet Zeki Sarikaya

Abstract

This paper aims to present a new refinement of the Jensen inequality specifically for convex functions. Building on this refinement, the paper derives various related inequalities, with a particular focus on Bullen's inequality and Ostrowski's inequality. Furthermore, it explores practical applications of these derived inequalities in the context of mean inequalities, providing a deeper understanding and broader utility of these mathematical concepts.

Keywords

Convex function, Bullen inequality, Jensen inequality, Ostrowski inequality and Special means

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