Advances in Operator Theory

On Zipf-Mandelbrot entropy and $3$-convex functions

Sadia Khalid, Đilda Pečarić, and Josip Pečarić

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‎‎‎‎‎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.

Article information

Adv. Oper. Theory, Volume 4, Number 4 (2019), 724-737.

Received: 13 October 2018
Accepted: 1 February 2019
First available in Project Euclid: 15 May 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 26A48‎ ‎26A51‎ 26D15: Inequalities for sums, series and integrals

Shannon entropy‎ ‎‎Zipf-Mandelbrot entropy‎ ‎divided difference ‎$n$-convex function‎ $n$-exponential convexity logarithmic convexity‎


Khalid, Sadia; Pečarić, Đilda; Pečarić, Josip. On Zipf-Mandelbrot entropy and $3$-convex functions. Adv. Oper. Theory 4 (2019), no. 4, 724--737. doi:10.15352/aot.1810-1426.

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