In this note, by O. Hadzić's [4] fixed point theorem for multifunctions in not necessarily locally convex topological vector spaces, we obtain a theorem of Iohvidov--Fan's type for multifunctions and give some its applications. Our results generalizes some results of I. S. Iolividov [7], Ky Fan [3], Felix Browder [1] and Olga Hadzić [5].