The purpose of this paper is to obtain some general coincidence theorems which generalize and improve some existence theorems of fixed point for multi - valued and single valued mappings in some previous papers. A generalization of the famous Fan - Kakutani theorem in also given.  得出了几个新的一般性的重合定理,它是许多已有论文中相应的单值(SV)和多值不动点定理的推广,同时也是著名的Fan-Kakutani定理的推广。