I have a sequence of integers meeting the following inequality: $u_n \leq \frac{u_{n-1}+u_{n+1}}{2} + \frac{1}{2}$. In other words, the sequence is "approximately convex", and the difference comes essentially from the fact that we are working with integers. For example, (2, 2, 1, 1) is not convex but is "approximately convex" in the above sense. It looks like $\frac{1}{2}$-Jensen-convexity, but I am not sure.
Some context: it comes from an optimization problem where the real solution is a geometric sequence, and the integer solution $(u_n)$ tries its best to "mimic" some properties of a geometric sequence (without being a rounding of it). I would like to convey the message that $(u_n)$ has properties that are not so far from those of a geometric sequence: for example, $(u_n)$ is non-increasing and "approximately convex".
