Generalized Steffensen's inequality by Lidstone interpolation and Montogomery's identity

Abstract

By using a Lidstone interpolation, Green's function and Montogomery's identity, we prove a new generalization of Steffensen's inequality. Some related inequalities providing generalizations of certain results given in (J. Math. Inequal. 9(2):481-487, 2015) have also been obtained. Moreover, from these inequalities, we formulate linear functionals and describe their properties.

Keywords: ( n + 1 ) -convex function at a point; Green’s function; Montogomery’s identity; Steffensen’s inequality.