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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: Stability of common fixed points in uniform spaces | Mishra et al. Fixed Point Theory and Applications 2011 2011 37 http www.fixedpointtheoryandapplications.eom content 2011 1 37 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Stability of common fixed points in uniform spaces Swaminath Mishra1 Shyam Lal Singh2 and Simfumene Stofile1 Correspondence smishra@wsu.ac. za department of Mathematics Walter Sisulu University Mthatha 5117 South Africa Full list of author information is available at the end of the article Abstract Stability results for a pair of sequences of mappings and their common fixed points in a Hausdorff uniform space using certain new notions of convergence are proved. The results obtained herein extend and unify several known results. AMS MOS Subject classification 2010 47H10 54H25. Keywords Stability fixed point uniform space J-Lipschitz Springer 1 Introduction The relationship between the convergence of a sequence of self mappings Tn of a metric resp. topological space X and their fixed points known as the stability or continuity of fixed points has been widely studied in fixed point theory in various settings cf. 1-18 . The origin of this problem seems into a classical result see Theorem 1.1 of Bonsall 6 see also Sonnenshein 18 for contraction mappings. Recall that a self-mapping f of a metric space X d is called a contraction mapping if there exists a constant k 0 k 1 such that d f x f y kd x y for all x y e X. Theorem 1.1. Let X d be a complete metric space and T and Tn n 1 2 . be contraction mappings of X into itself with the same Lipschitz constant k 1 and with fixed points u and un n 1 2 . respectively. Suppose that limn Tnx Tx for every x e X. Then limn un u. Subsequent results by Nadler Jr. 11 and others address mainly the problem of replacing the completeness of the space X by the existence of fixed points which was ensured otherwise by the completeness of X and various relaxations on the contraction constant k. In most of these results pointwise resp. .