Generalizations of cyclic refinements of jensen's inequality by lidstone's polynomial with applications in information theory

Jensen's inequality plays pivotal role in attaining divergence between probability distributions. Shannon, Relative and Zipf-Mandelbrot entropies have ample applications in many applied sciences, especially in information theory, biology, economics, etc. In the present paper, we have obtained new generalizations of cyclic refinements of Jensen's inequality using different new Green functions by employing Lidstone's polynomial. As an application of our obtained results we have given new entropic bounds. Also, we have established the connections between Shannon and Relative entropy with Zipf-Mandelbrot entropy. © ELEMENT, Zagreb.

Authors
Mehmood N.1 , Butt S.I.1 , Pečarić D.2 , Pečarić J. 3, 4 , Vukelić A.
Journal
Journal of Mathematical Inequalities
Publisher
Element D.O.O.
Number of issue
1
Language
English
Pages
249-271
Status
Published
Link
External link
DOI
10.7153/jmi-2020-14-17
Volume
14
Year
2020
Organizations
  • 1 COMSATS University Islamabad, Lahore Campus, Pakistan
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, Croatia
  • 3 Faculty Of Textile Technology, University Of Zagreb, Prilaz Baruna Filipovića 28a, Zagreb, 10000, Croatia
  • 4 RUDN University, Miklukho-Maklaya str.6, Moscow, 117198, Russian Federation
Keywords
2n-convex function; Divergence functional; Lidstone's polynomial; New green functions; Relative entropy; Shannon entropy; Zipf-mandelbrot entropy
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/64950/
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