Journal of Inequalities and Applications (Aug 2019)
RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory
Abstract
Abstract In the presented paper, Levinson’s inequality for 3-convex function is generalized by using two Green’s 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 f-divergence, Rényi divergence, Rényi entropy, Shannon entropy, and Zipf–Mandelbrot law.
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