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Scholars Journal of Physics, Mathematics and Statistics | Volume-1 | Issue-02
On Some Common Fixed Point Theorems for Certain Contractive Mappings in Cone Metric Spaces
A.K. Dubey, Rohit Verma
Published: Nov. 17, 2014 |
103
79
DOI: 10.36347/sjpms
Pages: 99-103
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Abstract
The aim of this paper is to establish the generalization of T-Reich and T-Rhoades type mappings on complete
cone metric spaces. Huang and Zhang introduce the notion of cone metric spaces. He replaced real number system by
ordered Banach space and gave the condition in the setting of cone metric spaces. These authors also described the
convergence of sequences in the cone metric spaces and introduce the corresponding notion of completeness. The study
of fixed point theorems in such spaces is followed by many researchers. In the present paper this study has been extended
to analyse the existence and uniqueness of common fixed points of T-Reich contractive mappings defined on a complete
cone metric space (�, �) as well as T-Rhoades contractive mappings. These results generalize and extend the existing
fixed point theorems available in the literature.
Keywords: Fixed point, complete cone metric spaces, sequentially convergent