2015•Advances in Inequalities and ApplicationsRequires access

Refinements of the classical Jensen’s inequality coming from refinements of the discrete Jensen’s inequality

László Horváth, Josip E. Pečarić

Abstract

In this paper new refinements of classical Jensen’s inequality are obtained by using some refinements of discrete Jensen’s inequality. To apply our refinements, new quasi-arithmetic means are introduced, the properties of these means are studied, and refinements of the left hand side of the Hermite-Hadamard inequality are given.

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Key concepts: Jensen's inequality, Mathematics, Inequality of arithmetic and geometric means, Inequality, Log sum inequality, Rearrangement inequality, Kantorovich inequality, Hölder's inequality