Various types of 𝜙A-spaces (X, D; {𝜙A}A∈⟨D⟩) are simply G-convex spaces. Various types of generalized KKM maps on 𝜙A-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of 𝜙A-spaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on 𝜙A-spaces.