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We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal. These theorems generalize the recent results of Huang and Zhang (2007), Abbas and Jungck (2008), and Vetro (2007). Furthermore as corollaries, we obtain recent results of Rezapour and Hamlborani (2008). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space (which is not necessarily normal) are obtained. By adapting Assad-Kirk's method the existence of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty. Examples show that the obtained results are proper extensions of the existing ones. [ABSTRACT FROM AUTHOR]

In this paper, the concept of a cone bv(s)-metric space over Banach algebra is introduced as a generalization of metric spaces, rectangular metric spaces, b-metric spaces, rectangular b-metric spaces, v-generalized metric spaces, cone b-metric spaces over Banach algebra and rectangular cone b-metric spaces over Banach algebra. We also give Banach and, Kannan fixed point results in cone bv(s)-metric spaces over Banach algebra. Some examples are provided as well. [ABSTRACT FROM AUTHOR]

Recently, Chao Wang, Jinghao Zhu, Bogko Damjanovid, Liang-gen Hu [Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces, Applied Mathematics and Computation 215 (2009) 1522-1525] proved some results for an Ishikawa type iteration process with errors, which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces. The aim of this paper is to consider this in the frame of abstract (cone) metric spaces. We extend some fixed point results of these mappings from complete generalized convex metric spaces to convex abstract metric spaces with the solid cone. Also, we have improved some results. Four examples are included. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples. [ABSTRACT FROM AUTHOR]