tailieunhanh - Báo cáo hóa học: " Research Article Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems"

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 Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 170253 17 pages doi 2010 170253 Research Article Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems Zoran Kadelburg 1 Stojan Radenovic 2 and Vladimir Rakocevic3 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 3 Department of Mathematics Faculty of Sciences and Mathematics University ofNis ViSegradska 33 18000 Nis Serbia Correspondence should be addressed to Stojan Radenovic sradenovic@ Received 18 December 2009 Revised 14 July 2010 Accepted 19 July 2010 Academic Editor Hichem Ben-El-Mechaiekh Copyright 2010 Zoran 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. We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points known from the theory of normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones. 1. Introduction Ordered normed spaces and cones have applications in applied mathematics for instance in using Newton s approximation method 1-4 and in optimization theory 5 . X-metric and X-normed spaces were introduced in the mid-20th century 2 see also 3 4 6 by using an ordered Banach space instead of the set of real numbers as the codomain for a metric. Huang and Zhang 7 reintroduced such spaces under the name of cone metric spaces but went further defining convergent and Cauchy sequences in the terms of interior points of the underlying cone. These and other authors see . 8-22 .