Levinson-type inequalities via new Green functions and Montgomery identity

Abstract

In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, a new functional is introduced based on f{\mathfrak{f}} divergence and then some estimates for new functional are obtained. Some inequalities for Shannon entropies are obtained too.

Keywords

• levinson's inequality
• montgomery identity
• information theory
• 26d20
• 26d15
• 94a20