Generalization of the Levinson inequality with applications to information theory

Abstract

Abstract In the presented paper, Levinson’s inequality for the 3-convex function is generalized by using two Green functions. Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via the f-divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf–Mandelbrot law.

Keywords

• Levinson’s inequality
• Information theory