Advances in Operator Theory
- Adv. Oper. Theory
- Volume 4, Number 4 (2019), 724-737.
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.
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
Permanent link to this document
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
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. https://projecteuclid.org/euclid.aot/1557885622