Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 170253, 17 pages
doi:10.1155/2010/170253
Research Article

Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems

Zoran Kadelburg,1 Stojan Radenović,2 and Vladimir Rakočević3

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.

Abstract

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.