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 Fixed Point in Topological Vector Space-Valued Cone Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 604084 9 pages doi 2010 604084 Research Article Fixed Point in Topological Vector Space-Valued Cone Metric Spaces Akbar Azam 1 Ismat Beg 2 and Muhammad Arshad3 1 Department of Mathematics COMSATS Institute of Information Technology Islamabad Pakistan 2 Department of Mathematics Centre for Advanced Studies in Mathematics Lahore University of Management Sciences Lahore Pakistan 3 Department of Mathematics International Islamic University Islamabad Pakistan Correspondence should be addressed to Ismat Beg ibeg@ Received 16 December 2009 Accepted 2 June 2010 Academic Editor Jerzy Jezierski Copyright 2010 Akbar Azam 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. We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature. 1. Introduction and Preliminaries Many authors 1-16 studied fixed points results of mappings satisfying contractive type condition in Banach space-valued cone metric spaces. In a recent paper 17 the authors obtained common fixed points of a pair of mapping satisfying generalized contractive type conditions without the assumption of normality in a class of topological vector space-valued cone metric spaces which is bigger than that of studied in 1-16 . In this paper we continue to study fixed point results in topological vector space valued cone metric spaces. Let E t be always a topological vector space TVS and P a subset of E. Then P is called a cone whenever i P is closed nonempty and P Ỷ 0 ii ax by e P for all x y e P and nonnegative real numbers a b iii P n -P 0 . For a given cone P Q E we can define a partial ordering with .
