Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 170253, 17 pages
Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems
1Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia
2Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
3Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
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.