Endpoints of multi-valued generalized weak contraction mappings

Let (X,d)(X,d) be a complete metric space, and let T:X→Pcl,bd(X) be a multi-valued generalized weak contraction mapping. Then TT has a unique endpoint if and only if TT has the approximate endpoint property. Our results extend previous results given by Ćirić (1971) [15], Nadler (1969) [11], Daffer and Kaneko (1995) [9] and Amini-Harandi (2010) [8].