tailieunhanh - Báo cáo hóa học: Research Article Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings

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 Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 28619 8 pages doi 2007 28619 Research Article An Iteration Method for Nonexpansive Mappings in Hilbert Spaces Lin Wang Received 22 August 2006 Revised 2 November 2006 Accepted 2 November 2006 Recommended by Nan-Jing Huang In real Hilbert space H from an arbitrary initial point x0 e H an explicit iteration scheme is defined as follows xn 1 anxn 1 - an Tin 1 xn n 0 where Tin 1 xn Txn -Ản 1 F Txn T H H is a nonexpansive mapping such that F T x e K Tx x is nonempty F H H is a n-strongly monotone and k-Lipschitzian mapping an c 0 1 and An c 0 1 . Under some suitable conditions the sequence xn is shown to converge strongly to a fixed point of T and the necessary and sufficient conditions that xn converges strongly to a fixed point of T are obtained. Copyright 2007 Lin Wang. 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 H be a Hilbert space with inner product and norm II II. A mapping T H H is said to be nonexpansive if II Tx - Ty II x - y II for any x y e H .A mapping F H H is said to be n-strongly monotone if there exists constant n 0 such that Fx - Fy x - y n x - y II2 for any x y e H. F H H is said to be k-Lipschitzian if there exists constant k 0 such that Fx - Fyll k x - y II for any x y e H. The interest and importance of construction of fixed points of nonexpansive mappings stem mainly from the fact that it may be applied in many areas such as imagine recovery and signal processing see . 1-3 . Iterative techniques for approximating fixed points of nonexpansive mappings have been studied by various authors see . 1 4-10 etc. using famous Mann iteration method Ishikawa iteration method and many other iteration methods such as viscosity approximation method 6 and CQ method 7 . Let F H