Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial

Abstract

Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.

Keywords

• steffensen’s inequality
• generalizations
• n-convex functions
• abel-gontscharoff polynomial
• ostrowski-type inequality
• grüss-type inequality
• primary 26d15
• secondary 26a51