tailieunhanh - Báo cáo hóa học: "Research Article Some Coupled Fixed Point Theorems 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 Some Coupled Fixed Point Theorems in Cone Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 125426 8 pages doi 2009 125426 Research Article Some Coupled Fixed Point Theorems in Cone Metric Spaces F. Sabetghadam 1 H. P. Masiha 1 and A. H. Sanatpour2 1 Department of Mathematics K. N. Toosi University of Technology Tehran 16315-1618 Iran 2 Department of Mathematics Tarbiat Moallem University Tehran 15618-36314 Iran Correspondence should be addressed to H. P. Masiha masiha@ Received 17 July 2009 Revised 23 September 2009 Accepted 28 September 2009 Recommended by Jerzy Jezierski We prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces. Copyright 2009 F. Sabetghadam 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 Recently Huang and Zhang in 1 generalized the concept of metric spaces by considering vector-valued metrics cone metrics with values in an ordered real Banach space. They proved some fixed point theorems in cone metric spaces showing that metric spaces really doesnot provide enough space for the fixed point theory. Indeed they gave an example of a cone metric space X d and proved existence of a unique fixed point for a selfmap T of X which is contractive in the category of cone metric spaces but is not contractive in the category of metric spaces. After that cone metric spaces have been studied by many other authors see 1-9 and the references therein . Regarding the concept of coupled fixed point introduced by Bhaskar and Laksh-mikantham 10 we consider the corresponding definition for the mappings on complete cone metric spaces and prove some coupled fixed point theorems in the next section. First we recall some standard notations and definitions in cone metric spaces. A cone P is a subset .