A new iteration scheme for approximating fixed points of nonexpansive mappings

Approximating fixed points of generalized nonexpansive mappings

New iteration process for approximating fixed points in Banach spaces

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...

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, . . ...