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 An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 723203 8 pages doi 2009 723203 Research Article An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions M. Asadi 1 H. Soleimani 1 and S. M. Vaezpour2 3 1 Department of Mathematics Science and Research Branch Islamic Azad University IAU 14778 93855 Tehran Iran 2 Department of Mathematics Amirkabir University of Technology 15916 34311 Tehran Iran 3 Department of Mathematics Newcastle University Newcastle NSW 2308 Australia Correspondence should be addressed to S. M. Vaezpour vaez@ Received 16 April 2009 Revised 19 August 2009 Accepted 22 September 2009 Recommended by Marlene Frigon In this paper at first we introduce a new order on the subsets of cone metric spaces then using this definition we simplify the proof of fixed point theorems for contractive set-valued maps omit the assumption of normality and obtain some generalization of results. Copyright 2009 M. Asadi 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 Preliminary Cone metric spaces were introduced by Huang and Zhang 1 . They replaced the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfying different contractions 1 . The study of fixed point theorems in such spaces followed by some other mathematicians see 2-8 . Recently Wardowski 9 was introduced the concept of set-valued contractions in cone metric spaces and established some end point and fixed point theorems for such contractions. In this paper at first we will introduce a new order on the subsets of cone metric spaces then using this definition we simplify the proof of fixed point theorems for contractive set-valued maps omit the assumption of normality and obtain some .