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

Nasir Mehmood; Saad Ihsan Butt; Ðilda PečarićJosip Pečarić

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

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

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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.

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来源
《Demonstratio Mathematica》 |2018年第1期|112-130|共19页
作者
Nasir Mehmood; Saad Ihsan Butt; Ðilda PečarićJosip Pečarić;
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作者单位

Department of Mathematics, Institute of Information Technology;

Catholic University of Croatia;

Faculty of Textile Technology, University of ZagrebRUDN University;

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正文语种英语
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n-convex function; Hermite interpolating polynomial; new Green functions; Shannon entropy; Relative entropy; Zipf-Mandelbrot entropy;

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

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