tailieunhanh - Báo cáo hóa học: "Research Article Hybrid Iteration Method for Fixed Points of Nonexpansive Mappings in Arbitrary Banach Spaces"

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 Hybrid Iteration Method for Fixed Points of Nonexpansive Mappings in Arbitrary Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 64306 7 pages doi 2007 64306 Research Article Hybrid Iteration Method for Fixed Points of Nonexpansive Mappings in Arbitrary Banach Spaces M. O. Osilike F. O. Isiogugu and P. U. Nwokoro Received 20 June 2007 Accepted 23 November 2007 Recommended by Nanjing Huang We prove that recent results of Wang 2007 concerning the iterative approximation of fixed points of nonexpansive mappings using a hybrid iteration method in Hilbert spaces can be extended to arbitrary Banach spaces without the strong monotonicity assumption imposed on the hybrid operator. Copyright 2007 M. O. Osilike et al. 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 E be a real Banach space. A mapping T E E is said to be L-Lipschitzian if there exists L 0 such that Tx - Tyll L x - yll Vx y e E. T is said to be nonexpansive if L 1 in . Several authors have studied various methods for the iterative approximation of fixed points of nonexpansive mappings. Recently Wang 1 studied the following iteration method in Hilbert spaces. The hybrid iteration method. Let H be a Hilbert space T H- H a nonexpansive mapping withF T x e H Tx x 0 andF H - H an L-Lipschitzian mapping which is also n-strongly monotone where T is n-strongly monotone if there exists n 0 such that Tx Ty x y n x y 2 Vx y e H. 2 Fixed Point Theory and Applications Let an 1 and An 1 be real sequences in 0 1 and p 0 then the sequence xn is generated from an arbitrary x1 e H by Xn 1 anXn 1 - an TẢrl 1 Xn n 1 where TẦn 1 xn Txn - Ản 1pF Txn p 0. Wang s work was motivated by earlier results of Xu and Kim 2 and Yamada 3 in addition to several other related results. Using this iteration method Wang proved the following main results. Lemma see 1 page 3 . Let