tailieunhanh - Báo cáo hóa học: "Research Article Construction of Fixed Points by Some Iterative Schemes"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Construction of Fixed Points by Some Iterative Schemes | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 612491 17 pages doi 2009 612491 Research Article Construction of Fixed Points by Some Iterative Schemes A. El-Sayed Ahmed1 2 and A. Kamal3 1 Mathematics Department Faculty of Science Sohag University Sohag 82524 Egypt 2 Mathematics Department Faculty of Science Taif University . Box 888 El-Hawiyah El-Taif5700 Saudi Arabia 3 Mathematics Department The High Institute of Computer Science Al-Kawser City 82524 Sohag Egypt Correspondence should be addressed to A. El-Sayed Ahmed ahsayed80@ Received 23 October 2008 Revised 5 February 2009 Accepted 23 February 2009 Recommended by Massimo Furi We obtain strong convergence theorems of two modifications of Mann iteration processes with errors in the doubly sequence setting. Furthermore we establish some weakly convergence theorems for doubly sequence Mann s iteration scheme with errors in a uniformly convex Banach space by a Frechet differentiable norm. Copyright 2009 A. El-Sayed Ahmed and A. Kamal. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let X be a real Banach space and let C be a nonempty closed convex subset of X. A selfmapping T C C is said to be nonexpansive if Tx- Ty x-y for all x y e C. A point x e C is a fixed point of T provided Tx x. Denote by Fix T the set of fixed points of T that is Fix T x e C Tx x . It is assumed throughout this paper that T is a nonexpansive mapping such that Fix T f 0. Construction of fixed points of nonexpansive mappings is an important subject in the theory of nonexpansive mappings and its applications in a number of applied areas in particular in image recovery and signal processing see 1-3 . One way to overcome this difficulty is to use Mann s iteration method that produces a sequence xn via the