© Hindawi Publishing Corp. APPROXIMATING FIXED POINTS OF NONEXPANSIVE TYPE MAPPINGS

Abstract. In a uniformly convex Banach space, the convergence of Ishikawa iterates to a unique fixed point is proved for nonexpansive type mappings under certain conditions. 2000 Mathematics Subject Classification. 47H10, 54H25. 1. Introduction. Let D be a nonempty, closed, and convex subset of a uniformly convex Banach space B, and T: D → D with fixed point set F(T). Recently, Ghosh and Debnath [1] introduced the generalized versions of the conditions of Senter and Dotson [6] as: the mapping T with F(t) = ∅ is said to satisfy the following conditions. Condition 1.1. If there exists a nondecreasing function f: [0,∞) → [0,∞) wit