tailieunhanh - Báo cáo hóa học: "Research Article Some Extensions of Banach’s Contraction Principle in Complete 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 Some Extensions of Banach’s Contraction Principle in Complete Cone Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 768294 11 pages doi 2008 768294 Research Article Some Extensions of Banach s Contraction Principle in Complete Cone Metric Spaces P. Raja and S. M. Vaezpour Department of Mathematics and Computer Sciences Amirkabir University of Technology . Box 15914 Hafez Avenue Tehran Iran Correspondence should be addressed to S. M. Vaezpour vaez@ Received 10 December 2007 Revised 2 June 2008 Accepted 23 June 2008 Recommended by Billy Rhoades In this paper we consider complete cone metric spaces. We generalize some definitions such as c-nonexpansive and c 1 -uniformly locally contractive functions -closure c-isometric in cone metric spaces and certain fixed point theorems will be proved in those spaces. Among other results we prove some interesting applications for the fixed point theorems in cone metric spaces. Copyright 2008 P. Raja and S. M. Vaezpour. 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 study of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity for example see 1-5 and it has a wide range of applications in different areas such as nonlinear and adaptive control systems parameterize estimation problems fractal image decoding computing magnetostatic fields in a nonlinear medium and convergence of recurrent networks see 6-10 . Recently Huang and Zhang generalized the concept of a metric space replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfying different contractive conditions 11 . The study of fixed point theorems in such spaces is followed by some other mathematicians see 12-15 . The aim of this paper is to generalize some definitions such