Abstract. A common fixed point theorem is proved for a multifunction, not necessarily convex valued, with open fibres and a family of commuting affine continuous mappings each of which commutes strongly with the multifunction. As a consequence of this result, a Browder's fixed point theorem for convex valued multifunction with open fibres is obtained. Also, a common fixed point theorem due to Itoh and Takahashi is generalized to a common fixed point theorem for a Kakutani factorizable multifunction and a family of commuting continuous affine mappings each of which commutes with all the factors of the factorizable multifunction.

AMS Subject Classification (1991): 47H10; 54H25

Received July 19, 1995 and in revised form March 7, 1996. (Registered under 5726/2009.)