A function that is never above its linear interpolation. Mathematically, a function f (x) is a convex over a convex set S, if or any two points x₁ and x₂ in S and for any 0 ≤ α ≤ 1, f [αx₁ + (1 − α)x₂] ≤ αf (x₁) + (1 − α) αf (x₂).