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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 542=24, 2020.

Original scientific paper

https://doi.org/10.21857/mzvkptqwg9

Combinatorial extensions of Popoviciu's inequality via Abel-Gontscharoff polynomial with applications in information theory

Saad Ihsan Butt orcid id orcid.org/0000-0001-7192-8269 ; Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Tahir Rasheed ; Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Đilda Pečarić ; Catholic University of Croatia, Ilica 242, Zagreb, Croatia
Josip Pečarić ; RUDN University, Miklukho-Maklaya str.6, 117198 Moscow, Russia

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Abstract

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.

Keywords

Popoviciu’s inequality; n-convex function; new Green functions; Grüss and Ostrowski inequality; divergence functional; Shannon Entropy; Kullback-Liebler distance.

Hrčak ID:

243438

URI

https://hrcak.srce.hr/243438

Publication date:

15.9.2020.

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