Consider the definition of convex functions:
$$
f(tx+(1-t)y) \le t f(x)+(1-t)f(y)
$$
It is easy to show the definition of the convexity on sets with respect to the above definition (Specifically for a convex hull of some points $x_1, ...., x_n$, it is the points $\sum_i \alpha_i x_i$ and $ \sum_i \alpha_i = 1 $).
Consider the definition of strong convex functions: $$ f(tx+(1-t)y) \le t f(x)+(1-t)f(y) - \frac{1}{2} m t(1-t) \|x-y\|_2^2 $$ for some $m > 0$. How can we reinterpret this definition for sets (or discrete points)?
I do not fully understand what you would like to ask. However, a possible answer could be the following.
A set $A$ is strongly convex, if there is some $m > 0$ with $$ x,y \in A \;\Rightarrow\; \lambda \, x + (1-\lambda) \, y + m \, \lambda \, (1-\lambda) \, \mathbb{B} \subset A, $$ where $\mathbb{B}$ is the unit ball. I must admit that I do not know if this definition is used anywhere.