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December 2021 Analysis of convexity results for discrete fractional nabla operators
Rajendra Dahal, Christopher S. Goodrich
Rocky Mountain J. Math. 51(6): 1981-2001 (December 2021). DOI: 10.1216/rmj.2021.51.1981

Abstract

We investigate the relationship between the sign of the discrete fractional difference (aνf)(t) and the convexity of the function f in the case where 2<ν<3. We focus on the scenario in which (aνf)(t) satisfies a negative lower bound. Our analytical results are complemented with numerical simulations, the latter providing insight beyond what we are able to produce analytically.

Citation

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Rajendra Dahal. Christopher S. Goodrich. "Analysis of convexity results for discrete fractional nabla operators." Rocky Mountain J. Math. 51 (6) 1981 - 2001, December 2021. https://doi.org/10.1216/rmj.2021.51.1981

Information

Received: 26 February 2021; Accepted: 8 May 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1981

Subjects:
Primary: 26A51‎ , 33F05 , 39A12 , 65D15 , 65Q20
Secondary: 39A99 , ‎39B62

Keywords: convexity , Discrete fractional calculus , Gamma function , numerical approximation , sequential difference

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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