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2016•Journal of Inequalities and ApplicationsOpen access

On an upper bound for Sherman’s inequality

Slavica Ivelić Bradanović, Naveed ‎Latif‎, Josip E. Pečarić

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Abstract

Considering a weighted relation of majorization, Sherman obtained a useful generalization of the classical majorization inequality. The aim of this paper is to extend Sherman’s inequality to convex functions of higher order. An upper bound for Sherman’s inequality, as well as for generalized Sherman’s inequality, is given with some applications. As easy consequences, some new bounds for Jensen’s inequality can be derived.

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What this paper is about

Considering a weighted relation of majorization, Sherman obtained a useful generalization of the classical majorization inequality. The aim of this paper is to extend Sherman’s inequality to convex functions of higher order. An upper bound for Sherman’s inequality, as well as for generalized Sherman’s inequality, is given with some applications. As easy consequences, some new bounds for Jensen’s inequality can be derived.

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Available abstract

Considering a weighted relation of majorization, Sherman obtained a useful generalization of the classical majorization inequality. The aim of this paper is to extend Sherman’s inequality to convex functions of higher order. An upper bound for Sherman’s inequality, as well as for generalized Sherman’s inequality, is given with some applications. As easy consequences, some new bounds for Jensen’s inequality can be derived.

Key concepts: Mathematics, Majorization, Inequality, Generalization, Jensen's inequality, Upper and lower bounds, Convex function, Kantorovich inequality

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