A characterization of convex function Original Research Article

If C ⊆ Rn be a nonempty convex set, then f: C → R is convex function if and only if it is a quasiconvex function on C and there exists some α ∈ (0, 1) such that f(ax+1(1−α)y)≤αf(x)+(1−α)f(y), ∀x,y ϵC.