On Zipf-Mandelbrot entropy and 3-convex functions

In this paper, we present some interesting results related to the bounds of Zipf-Mandelbrot entropy and the 3-convexity of the function. Further, we define linear functionals as the nonnegative differences of the obtained inequalities and we present mean value theorems for the linear functionals. Finally, we discuss the n-exponential convexity and the log-convexity of the functions associated with the linear functionals. © 2019 by the Tusi Mathematical Research Group.

Authors
Khalid S.1 , Pečarić D.2 , Pečarić J. 3
Journal
Advances in Operator Theory
Publisher
Tusi Mathematical Research Group (TMRG)
Number of issue
4
Language
English
Pages
724-737
Status
Published
Link
External link
DOI
10.15352/aot.1810-1426
Volume
4
Year
2019
Organizations
  • 1 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
  • 3 Rudn University, Miklukho-Maklaya str., Moscow, 6117198, Russian Federation
Keywords
Divided difference; Logarithmic convexity; N- convex function; N-exponential convexity; Shannon entropy; Zipf-Mandelbrot entropy
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38542/
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