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Demonstratio Mathematica

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Volume 51, Issue 1


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

Nasir Mehmood / Saad Ihsan Butt / Ðilda Pečarić / Josip Pečarić
  • Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia
  • RUDN University, Miklukho-Maklaya str.6, 117198 Moscow, Russian Federation
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Published Online: 2018-05-31 | DOI: https://doi.org/10.1515/dema-2018-0011


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.

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

MSC 2010: 26A51; 26D15; 26E60; 94A17; 94A15


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About the article

Received: 2017-01-07

Accepted: 2018-04-03

Published Online: 2018-05-31

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 112–130, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0011.

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© 2018 Nasir Mehmood et al. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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