tailieunhanh - Báo cáo hóa học: "Research Article Strict Contractive Conditions and Common Fixed Point Theorems in Cone Metric Spac"

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 Strict Contractive Conditions and Common Fixed Point Theorems in Cone Metric Spac | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 173838 14 pages doi 2009 173838 Research Article Strict Contractive Conditions and Common Fixed Point Theorems in Cone Metric Spaces Z. Kadelburg 1 S. Radenovic 2 and B. Rosic2 1 Faculty of Mathematics University of Belgrade Studentski trg 16 11000 Beograd Serbia 2 Faculty of Mechanical Engineering University of Belgrade Kraljice Marije 16 11120 Beograd Serbia Correspondence should be addressed to S. Radenovic radens@ Received 22 June 2009 Accepted 9 September 2009 Recommended by Lech Gorniewicz A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property introduced recently in the work by Aamri and Moutawakil 2002 and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones. Copyright 2009 Z. Kadelburg 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 and Preliminaries Cone metric spaces were introduced by Huang and Zhang in 1 where they investigated the convergence in cone metric spaces introduced the notion of their completeness and proved some fixed point theorems for contractive mappings on these spaces. Recently in 2-6 some common fixed point theorems have been proved for maps on cone metric spaces. However in 1-3 the authors usually obtain their .