Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

In this paper, we study a multi-step iterative scheme with errors involving N nonexpansive mappings in the Banach space. Some weak and strong convergence theorems for approximation of common fixed points of nonexpansive mappings are proved using this iteration scheme. The results extend and improve the corresponding results of [1].

In this paper we consider the convergence of iterative processes for a family of multivalued nonexpansive mappings. Under somewhat different conditions the sequences of Noor, Mann and Ishikawa iterates converge to the common fixed point of the family of multivalued nonexpansive mappings.

In this paper we established strong and weak convergence theorems for a multi-step iterative scheme with errors for nonself asymptotically nonexpansive mappings in the real uniformly convex Banach space. Our results extend and improve the ones announced by Lin Wang [Lin Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. A...

The purpose of this article is to modify normal Mann’s iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.