Cerone's generalizations of Steffensen's inequality

Abstract

In this paper generalizations of Steensen's inequality with bounds involving any two subin-
tervals motivated by Cerone's generalizations are given. Furthermore, weaker conditions for Cerone's
generalization as well as for new generalizations obtained in this paper are given. Moreover, functionals
dened as the dierence between the left-hand and the right-hand side of this generalizations are studied
and new Stolarsky type means related to them are obtained.