Some common best proximity point theorems in a complete metric space. (English) Zbl 1489.54177
Summary: In this article, we prove the existence and uniqueness of common best proximity point for a pair of non-self mappings satisfying weak \(P\)-property in a complete metric space. Moreover, we prove the same for Kannan type mappings and \(C\)-contractive mappings using weak \(P\)-property by changing non-self mappings to self mappings in a complete metric space. We take much weaker conditions on the mappings to prove our results. An example is presented here to support our main result.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
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