Let C be a closed convex subset of a Hilbert space E. A mapping T on C is called a nonexpansive mapping if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. We denote by F T the set of fixed points of T . Browder, see 1 , proved that F T is nonempty provided that C is, in addition, bounded. Kirk in a very celebrated paper, see 2 , extended this result to the setting of reflexive Banach spaces with normal structure. Browder 3 initiated the investigation of an implicit method for approximating fixed points… CONTINUE READING