Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 173838, 14 pages
doi:10.1155/2009/173838
Research Article

Strict Contractive Conditions and Common Fixed Point Theorems in Cone Metric Spaces

Z. Kadelburg,1 S. Radenović,2 and B. Rosić2

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

Received 22 June 2009; Accepted 9 September 2009

Academic Editor: Lech Górniewicz

Copyright © 2009 Z. 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

A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property (E.A), introduced recently in the work by Aamri and Moutawakil (2002), and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones.