If f, g F(X) are convex, then f + g is convex f is

If f, g ∈ F(X) are convex, then
• f + g is convex
• αf is convex for every α ≥ 0
Therefore the set of convex functions on a set X is a cone in F(X). Moreover, if f is strictly convex, then
• f + g is strictly convex
• αf is strictly convex for every α > 0