Generalisations of Steffensen's inequality via Fink identity and related results

Abstract

Starting from the result given in [1] where the authors gave the extension of weighted Montgomery identity using Fink identity from [5], we give the generalizations of Steffensen inequality. Also, we investigate the exponential convexity of differences of the left-hand and right-hand side of these inequalities. Using these differences, we produce new exponentially convex functions. They are used in studying Stolarsky type means.