We investigate the relationship between the sign of the discrete fractional difference and the convexity of the function in the case where . We focus on the scenario in which 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.
"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