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Báo cáo hóa học: " Research Article Strong Convergence of a New Iteration for a Finite Family of Accretive Operators"

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 Strong Convergence of a New Iteration for a Finite Family of Accretive Operators | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 491583 15 pages doi 10.1155 2009 491583 Research Article Strong Convergence of a New Iteration for a Finite Family of Accretive Operators Liang-Gen Hu and Jin-Ping Wang Department of Mathematics Ningbo University Zhejiang 315211 China Correspondence should be addressed to Liang-Gen Hu hulianggen@yahoo.cn Received 9 March 2009 Revised 13 May 2009 Accepted 17 May 2009 Recommended by Mohamed A. Khamsi The viscosity approximation methods are employed to establish strong convergence of the modified Mann iteration scheme to a common zero of a finite family of accretive operators on a strictly convex Banach space with uniformly Gateaux differentiable norm. Our work improves and extends various results existing in the current literature. Copyright 2009 L.-G. Hu and J.-P. 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 E be a Banach space with dual space of E and let C a nonempty closed convex subset E. Let N 1 be a positive integer and let A 1 2 . N . We denote by J the normalized duality map from E to 2E defined by J x Ịx e E x x x 2 x 2 Vx e e . 1.1 A mapping T C C is said to be nonexpansive if Tx- Ty x-yll for all x y e C. A mapping f C C is called k-contraction if there exists a constant k e 0 1 such that f x - f y k x-yỊỊ Vx y e C. 1.2 In the last ten years many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see e.g. 1-20 . An operator A D A c E E is said to be accretive if xi - x2 xi - x2 s yi-y2 for all yi e Axi i 1 2 and s 0. If A is accretive and I is identity mapping then we define for each r 0 a nonexpansive single-valued mapping Jr R I rA D A by 2 Fixed Point Theory and Applications Jr I rA -1 which is called the .