COMMON FIXED POINT RESULTS WITH APPLICATIONS IN CONVEX METRIC SPACE (original) (raw)
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Common fixed point results with applications in convex metric spaces
Sufficient conditions for the existence of a common fixed point for uniformly C q − commuting mappings satisfying a generalized contractive conditions in the framework of a convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in the literature.
FIXED POINT THEOREM FOR COMMUTING MAPPING
It can be observed that completeness of a metric space is not enough to ensure the existence of fixed point for contractive mappings. So, fixed point theorems for such mappings require further restriction on the space or extra conditions have to be imposed on mappings or some restrictions imposed on its range. Edelstein had shown that compactness of the metric space (X,d) guarantees a unique fixed point for a contractive mapping on X. In this paper,the commutative maps are used as a tool for generalizing some of the results.
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