MODIFIED NOOR MULTISTEP ITERATIVE PROCESS WITH ERRORS FOR NONSELF ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS

Abstract

Many practical problems can be formulated as the xed point problem x = Tx,
where T is a nonexpansive mapping. Iterative methods as a powerful tool are often used to
approximating the xed point of such mapping, including Krasnoselskij iteration method,
Mann iteration method, Ishikawa iteration method and Noor iteration method etc,. The
purpose of this paper is to introduce a modi ed Noor multistep iterative process with errors
for approximating the common xed point of a nite family of nonself asymptotically quasi-
nonexpansive mappings. By using this iterative scheme, we prove several strong convergence
theorems for such mappings in uniformly convex Banach spaces. Our results improve and
extend some recent results in the literature.