New bounds of Popoviciu's difference via weighted Hadamard type inequalities with applications in information theory

Abstract

We generalize Popoviciu's inequality utilizing the theory of 4‐convex function under the effect of new Green functions. We formulate result for power means and quasi means. Also, we give applications in information theory by giving new estimations of generalized Csiszár divergence, Rényi divergence, Shannon entropy, Kullback–Leibler divergence, divergence, Zipf–Mandelbrot entropy, and Hybrid Zipf–Mandelbrot entropy.