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

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. Copyright q 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