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Báo cáo hóa học: " Review Article Some Generalizations of Fixed Point Theorems in Cone Metric Space"

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: Review Article Some Generalizations of Fixed Point Theorems in Cone Metric Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 657914 10 pages doi 10.1155 2009 657914 Review Article Some Generalizations of Fixed Point Theorems in Cone Metric Spaces J. O. Olaleru Mathematics Department University of Lagos Yaba Lagos Nigeria Correspondence should be addressed to J. O. Olaleru olaleru1@yahoo.co.uk Received 17 March 2009 Revised 15 July 2009 Accepted 29 August 2009 Recommended by Mohamed A. Khamsi We generalize extend and improve some recent fixed point results in cone metric spaces including the results of H. Guang and Z. Xian 2007 P. Vetro 2007 M. Abbas and G. Jungck 2008 Sh. Rezapour and R. Hamlbarani 2008 . In all our results the normality assumption which is a characteristic of most of the previous results is dispensed. Consequently the results generalize several fixed results in metric spaces including the results of G. E. Hardy and T. D. Rogers 1973 R. Kannan 1969 G. Jungck S. Radenovic S. Radojevic and V. Rakocevic 2009 and all the references therein. Copyright 2009 J. O. Olaleru. 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 The recently discovered applications of ordered topological vector spaces normal cones and topical functions in optimization theory have generated a lot of interest and research in ordered topological vector spaces e.g. see 1 2 . Recently Huang and Zhang 3 introduced cone metric spaces which is a generalization of metric spaces by replacing the real numbers with ordered Banach spaces. They later proved some fixed point theorems for different contractive mappings. Their results have been generalized by different authors e.g. see 47 . This paper generalizes extends and improves the results of all those authors. The following definitions are given in 3 . Let E be a real Banach space and P a subset of