Approximating fixed points of total asymptotically nonexpansive mappings

Approximating Fixed Points of Total Asymptotically Nonexpansive Mappings

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

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, . . ...