NEW BOUNDS FOR SHANNON, RELATIVE AND MANDELBROT ENTROPIES VIA ABEL-GONTSCHAROFF INTERPOLATING POLYNOMIAL

The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We use discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions and Abel-Gontschamff interpolating polynomial. As an application of our work, we establish connection among new entropic bounds for Shanon, Relative and Mandelbrot entropies.

Authors
Butt S.I.1 , Mehmood N.1 , Pecaric D.2 , Pecaric J. 3
Publisher
Element D.O.O.
Number of issue
4
Language
English
Pages
1283-1301
Status
Published
Volume
22
Year
2019
Organizations
  • 1 COMSATS Univ Islamabad, Lahore Campus, Lahore, Pakistan
  • 2 Catholic Univ Croatia, Ilica 242, Zagreb, Croatia
  • 3 RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia
Keywords
n-convex function; Abel-Gontscharoff interpolating polynomial; new Green functions; Shannon entropy; relative entropy; Zipf-Mandelbrot entropy
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55642/