Qualitative Properties of Nonlocal Discrete Operators

In this article, we prove new convexity results for nonlocal discrete operators across an entire region that covers sequential orders in two parameters. We review and extend current studies on the properties of positivity, monotonicity, and convexity, explore borderline cases, and provide new insights on such properties by means of original examples evidencing the sharpness of the results. Our method is based on the novel principle of transference. © 2022 John Wiley & Sons, Ltd.