#### Institution

Coastal Carolina University

#### 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) x (1,2).

A Uniformly Sharp Convexity Result for Discrete Fractional Sequential Differences

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) x (1,2).