Generalization of Steffensen's inequality for higher order convex function involving extensions of montgomery identities on time scales

Abstract

Generalizations of some Steffensen's inequalities for the class of higher order convex functions are obtained in present study. To prove the results, some preliminary lemmas are established by using extended Montgomery identities via Taylor's formula on time scales. Furthermore, Ostrowski type inequalities are also established, along with prove of optimization of the constant. Moreover, newly obtained results are discussed in discrete and quantum calculus as well.