Generalizations of Steffensen’s inequality via the extension of Montgomery identity

Abstract

In this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s inequality. Related Ostrowski type inequalities are also provided. Bounds for the reminders in new identities are given by using the Chebyshev and Grüss type inequalities.

Keywords

• steffensen’s inequality
• n-convex functions
• montgomery identity
• ostrowski-type inequality
• grüss-type inequality
• 26d15
• 26a51