Generalized Taylor’s Formula and Steffensen’s Inequality

Abstract

New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality and Faà di Bruno’s formula for higher order derivatives of the composition.

Keywords

• Steffensen’s inequality
• generalized Taylor’s formula
• Faà di Bruno’s formula
• Euler polynomial
• convex functions