On an upper bound for Sherman’s inequality

Abstract

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.

Keywords

• Sherman theorem
• Sherman inequality
• Jensen inequality
• Abel-Gontscharoff interpolating polynomial
• Ostrowski type inequality