New bounds for Shannon, Relative and Mandelbrot entropies via Hermite interpolating polynomial

Demonstratio mathematica

article

Nasir Mehmood¹  Saad Ihsan Butt¹  Ðilda Pečarić²  Josip Pečarić³ 

[1] Department of Mathematics, Institute of Information Technology;Catholic University of Croatia;Faculty of Textile Technology, University of Zagreb;RUDN University

关键词: n-convex function;    Hermite interpolating polynomial;    new Green functions;    Shannon entropy;    Relative entropy;    Zipf-Mandelbrot entropy;   

DOI  :  10.1515/dema-2018-0011

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

To procure inequalities for divergences between probability distributions, Jensen’s inequality is the key to success. Shannon, Relative and Zipf-Mandelbrot entropies have many applications in many applied sciences, such as, in information theory, biology and economics, etc. We consider discrete and continuous cyclic refinements of Jensen’s inequality and extend them from convex function to higher order convex function by means of different new Green functions by employing Hermite interpolating polynomial whose error term is approximated by Peano’s kernal. As an application of our obtained results, we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.

【 授权许可】

CC BY