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
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
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