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Báo cáo hóa học: " Research Article A New One-Step Iterative Process for Common Fixed Points in 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 A New One-Step Iterative Process for Common Fixed Points in Banach Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 548627 10 pages doi 10.1155 2008 548627 Research Article A New One-Step Iterative Process for Common Fixed Points in Banach Spaces Mujahid Abbas 1 Safeer Hussain Khan 2 and Jong Kyu Kim3 1 Mathematics Department Lahore University of Management Sciences Lahore 54792 Pakistan 2 Department of Mathematics and Physics Qatar University P.O. Box 2713 Doha Qatar 3 Department of Mathematics Education Kyungnam University Masan Kyungnam 631-701 South Korea Correspondence should be addressed to Jong Kyu Kim jongkyuk@kyungnam.ac.kr Received 26 September 2008 Accepted 22 October 2008 Recommended by Ram U. Verma We introduce a new one-step iterative process and use it to approximate the common fixed points of two asymptotically nonexpansive mappings through some weak and strong convergence theorems. Our process is computationally simpler than the processes currently being used in literature for the purpose. Copyright 2008 Mujahid Abbas 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 Throughout this paper N denotes the set of positive integers. Let E be a real Banach space C a nonempty convex subset of E. A mapping T C C is called asymptotically nonexpansive if there is a sequence kn c 1 to such that Tnx - Tny kn x - y Nx y e C Nn e N 1.1 where STO-1 kn - 1 TO. A point x e C is a fixed point of T provided that Tx x. To approximate the common fixed points of two mappings the following Ishikawa-type two-step iterative process is widely used see e.g. 1-9 and references cited therein x1 x e C xn 1 1 - ữn xn anSnyn 1.2 yn 1 - bn xn bnTnxn n e N where an and bn are in 0 1 satisfying certain conditions. Note that approximating fixed points of two mappings has a direct link with the minimization problem see e.g.