Generalizations of Levinson type inequalities via new Green functions with applications to information theory

Abstract

Abstract In this paper, four new Green functions are used to generalize Levinson-type inequalities for the class of 3-convex functions. The f-divergence, Renyi entropy, Renyi divergence, Shannon entropy, and the Zipf–Mandelbrot law are also used to apply the main results to information theory.

Keywords

• Csiszár divergence
• Green functions
• Levension’s inequality