Approximating Fixed Points of Nonexpansive Mappings by the Ishikawa Iteration Process

Approximating fixed points of generalized nonexpansive mappings

approximating fixed points of generalized nonexpansive mappings

Approximating Fixed Points of Nonexpansive Mappings

We consider a mapping S of the form S =α0I+α1T1+α2T2+···+αkTk, where αi ≥ 0, α0 > 0, α1 > 0 and ∑k i=0αi = 1. We show that the Picard iterates of S converge to a common fixed point of Ti (i = 1,2, . . . ,k) in a Banach space when Ti (i = 1,2, . . . ,k) are nonexpansive.

Approximating Fixed Points of Nonexpansive Mappings

Let D be a subset of a normed space X and T : D → X be a nonexpansive mapping. In this paper we consider the following iteration method which generalizes Ishikawa iteration process: xn+1 = t (1) n T (t (2) n T (· · ·T (t (k) n Txn + (1− t (k) n )xn + u (k) n ) + · · · ) +(1− t n )xn + u (2) n ) + (1− t (1) n )xn + u (1) n , n = 1, 2, 3 . . . , where 0 ≤ t (i) n ≤ 1 for all n ≥ 1 and i = 1, . . ...

Ishikawa Iteration Process with Errors for Nonexpansive Mappings

We study the construction and the convergence of the Ishikawa iterative process with errors for nonexpansive mappings in uniformly convex Banach spaces. Some recent corresponding results are generalized. 2000 Mathematics Subject Classification. 47H10, 40A05.