A general implicit iteration for finding fixed points of nonexpansive mappings

Abstract

The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. The strong convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the sequence of parameters. Our results extend and improve the results given by Ke and Ma Y. Ke, C. Ma, Fixed Point Theory Appl., 2015 (2015), 21 pages., Xu et al. H. K. Xu, M. A. Alghamdi, N. Shahzad, Fixed Point Theory Appl., 2015 (2015), 12 pages., and many others. © 2016 all rights reserved.