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Báo cáo hóa học: " Research Article On T -Stability of Picard Iteration in Cone Metric 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 On T -Stability of Picard Iteration in Cone Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 751090 6 pages doi 10.1155 2009 751090 Research Article On T-Stability of Picard Iteration in Cone Metric Spaces M. Asadi 1 H. Soleimani 1 S. M. Vaezpour 2 3 and B. E. Rhoades4 1 Department of Mathematics Science and Research Branch Islamic Azad University IAU Tehran 14778 93855 Iran 2 Department of Mathematics Amirkabir University of Technology Tehran 15916 34311 Iran 3 Department of Mathematics Newcastle University Newcastle NSW 2308 Australia 4 Department of Mathematics Indiana University Bloomington IN 46205 USA Correspondence should be addressed to S. M. Vaezpour vaez@aut.ac.ir Received 28 March 2009 Revised 28 September 2009 Accepted 19 October 2009 Recommended by Brailey Sims The aim of this work is to investigate the T-stability of Picard s iteration procedures in cone metric spaces and give an application. Copyright 2009 M. Asadi 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 and Preliminary Let E be a real Banach space. A nonempty convex closed subset P c E is called a cone in E if it satisfies the following i P is closed nonempty and P Ỷ 0 ii a b e R a b 0 and x y e P imply that ax by e P iii x e P and -x e P imply that x 0. The space E can be partially ordered by the cone P c E by defining x y if and only if y - x e P. Also we write x y if y - x e int P where int P denotes the interior of P. A cone P is called normal if there exists a constant K 0 such that 0 x y implies x Kllyll. In the following we always suppose that E is a real Banach space P is a cone in E and is the partial ordering with respect to P. Definition 1.1 see 1 . Let X be a nonempty set. Assume that the mapping d X X X E satisfies the following 2 Fixed Point Theory and Applications i 0 d x y for all x y e X and d x