Generalizations of Steffensen's inequality by Lidstone's polynomial and related results

Abstract

In this paper we obtain few valuable identities by using Lidstone's polynomial. Further, the identities were applied for constructing new  generalizations of Steffensen's inequality, namely for (2n) - convex and (2n + 1) - convex functions. In addition, using Cebysev and Gruss type inequalities we consider the bounds for the integrals in the perturben versions of the previously described identities. Moreover, related Ostrowski type inequalities are given.

Key words: Steffensen's inequality, generalizations, n-convex functions, Lidstone polynomial, Ostrowski-type inequality, Gruss-type inequality.