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Báo cáo hóa học: "Research Article Some Convergence Theorems of a Sequence in Complete Metric Spaces and Its Applications"

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 Some Convergence Theorems of a Sequence in Complete Metric Spaces and Its Applications | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 647085 10 pages doi 10.1155 2010 647085 Research Article Some Convergence Theorems of a Sequence in Complete Metric Spaces and Its Applications M. A. Ahmed and F. M. Zeyada Department of Mathematics Faculty of Science Assiut University Assiut 71516 Egypt Correspondence should be addressed to M. A. Ahmed mahmed68@yahoo.com Received 20 June 2009 Accepted 7 September 2009 Academic Editor Tomas Dominguez Benavides Copyright 2010 M. A. Ahmed and F M. Zeyada. 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. The concept of weakly quasi-nonexpansive mappings with respect to a sequence is introduced. This concept generalizes the concept of quasi-nonexpansive mappings with respect to a sequence due to Ahmed and Zeyada 2002 . Mainly some convergence theorems are established and their applications to certain iterations are given. 1. Introduction In 1916 Tricomi 1 introduced originally the concept of quasi-nonexpansive for real functions. Subsequently this concept has studied for mappings in Banach and metric spaces see e.g. 2-7 . Recently some generalized types of quasi-nonexpansive mappings in metric and Banach spaces have appeared. For example see Ahmed and Zeyada 8 Qihou 9-11 and others. Unless stated to the contrary we assume that X d is a metric space. Let T D c X X be any mapping and let F T be the set of all fixed points of T .If F X R where R is the set of all real numbers and if c e R set Lc x e X F x c . We use the symbol p to denote the usual Kuratowski measure of noncompactness. For some properties of p see Zeidler 12 pages 493-495 . For a given x0 e D the Picard iteration xn is determined by I Xn T Xn-1 Tn xo n e N where N is the set of all positive integers. If X is a normed space D is a convex set and T D D .