Levinson type inequalities for higher order convex functions via Abel–Gontscharoff interpolation

Abstract

Abstract In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel–Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for the functionals involving data points of two types.

Keywords

• m-convex function
• Levinson’s inequality
• Green functions