Generalizations of Levinson-type inequalities via new Green functions and Hermite interpolating polynomial

Abstract

Abstract In this study, Levinson-type inequalities for the class of n-convex ( n ≥ 3 $n \geq 3$ ) functions are generalized using new Green functions and the Hermite interpolating polynomial involving two types of data points. Some estimations for novel functionals are derived using f-divergence. Furthermore, different inequalities involving Shannon entropies are presented.

Keywords

• f-divergence
• Green functions
• Levension’s inequality