Combinatorial extensions of Popoviciu’s inequality via Abel-Gontscharoff polynomial with applications in information theory [Kombinatorna proširenja Popoviciuove nejednakosti preko Abel-Gontscharoffovih polinoma s primjenama u teoriji informacija]

We establish new refinements and improvements of Popoviciu’s inequality for n-convex functions using Abel-Gontscharoff interpolating polynomial along with the aid of new Green functions. We construct new inequalities for n-convex functions and compute new upper bounds for Ostrowski and Grüss type inequalities. As an application of our work in information theory, we give new estimations for Shannon, Relative and Zipf-Mandelbrot entropies using generalized Popoviciu’s inequality. © 2020 Croatian Academy of Sciences and Arts. All rights reserved.