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Autumn 2019 On Zipf-Mandelbrot entropy and $3$-convex functions
Sadia Khalid, Đilda Pečarić, Josip Pečarić
Adv. Oper. Theory 4(4): 724-737 (Autumn 2019). DOI: 10.15352/aot.1810-1426

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 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.

Citation

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Sadia Khalid. Đilda Pečarić. Josip Pečarić. "On Zipf-Mandelbrot entropy and $3$-convex functions." Adv. Oper. Theory 4 (4) 724 - 737, Autumn 2019. https://doi.org/10.15352/aot.1810-1426

Information

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

zbMATH: 07064101
MathSciNet: MR3949971
Digital Object Identifier: 10.15352/aot.1810-1426

Subjects:
Primary: 26A24
Secondary: 26A48, 26A51‎, 26D15

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 4 • Autumn 2019
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