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2019 A uniformly sharp convexity result for discrete fractional sequential differences
Rajendra Dahal, Christopher S. Goodrich
Rocky Mountain J. Math. 49(8): 2571-2586 (2019). DOI: 10.1216/RMJ-2019-49-8-2571

Abstract

We prove that a class of convexity-type results for sequential fractional delta differences is uniformly sharp. More precisely, we consider the sequential difference $\Delta _{1-\mu +a}^{\nu }\Delta _{a}^{\mu }f(t)$, for $t\in \mathbb {N}_{3+a-\mu -\nu }$, and demonstrate that there is a strong connection between the sign of this function and the convexity or concavity of $f$ if and only if the pair $(\mu ,\nu )$ lives in a particular subregion of the parameter space $(0,1)\times (1,2)$.

Citation

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Rajendra Dahal. Christopher S. Goodrich. "A uniformly sharp convexity result for discrete fractional sequential differences." Rocky Mountain J. Math. 49 (8) 2571 - 2586, 2019. https://doi.org/10.1216/RMJ-2019-49-8-2571

Information

Published: 2019
First available in Project Euclid: 31 January 2020

zbMATH: 07163187
MathSciNet: MR4058338
Digital Object Identifier: 10.1216/RMJ-2019-49-8-2571

Subjects:
Primary: 26A51‎, 39A70, ‎39B62
Secondary: 26A33, 39A12, 39A99.

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 8 • 2019
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