# On Zipf-Mandelbrot entropy and 3-convex functions

Document Type: Original Article

Authors

2 Catholic University of Croatia, Croatia

3 Rudn University, Russia

Abstract

‎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 non-negative 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.

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### History

• Receive Date: 13 October 2018
• Revise Date: 01 February 2019
• Accept Date: 01 February 2019