tailieunhanh - Báo cáo hóa học: " New Methods with Perturbations for NonExpansive Mappings in Hilbert Spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : New Methods with Perturbations for NonExpansive Mappings in Hilbert Spaces | Yao and Shahzad Fixed Point Theory and Applications 2011 2011 79 http content 2011 1 79 RESEARCH Fixed Point Theory and Applications a SpringerOpen Journal Open Access New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces Yonghong Yao1 and Naseer Shahzad2 Correspondence nshahzad@kau. department of Mathematics King Abdul Aziz University P. O. B. 80203 Jeddah 21589 Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper we suggest and analyze two iterative algorithms with perturbations for non-expansive mappings in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to a fixed point of some non-expansive mapping. 2000 Mathematics Subject Classification 47H09 47H10. Keywords Fixed point non-expansive mapping iterative method projection 1. Introduction Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping T C C is said to be non-expansive if Tx Iy x y for all x y e C. Denote by Fix T the set of fixed points of T that is Fix T x e C Tx x . Recently iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem partial differential equations image recovery and signal processing see 1-34 and the references therein. There are perturbations always occurring in the iterative processes because the manipulations are inaccurate. It is no doubt that researching the convergent problems of iterative methods with perturbation members is a significant job. It is our purpose in this paper that we suggest and analyze two iterative algorithms with errors for non-expansive mappings in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to a fixed point of some non-expansive mapping. 2. Preliminaries Let H be a real Hilbert space with inner product and .