Best proximity point and best proximity coupled point in a complete metric space with (\(P\))-property. (English) Zbl 1462.54104
Summary: In this paper, we utilize the concept of \((P)\)-property, weak \((P)\)-property and the comparison function to introduce and prove an existence and uniqueness theorem of a best proximity point. Also, we introduce the notion of a best proximity coupled point of a mapping \(F:X\times X\to X\). Using this notion and the comparison function to prove an existence and uniqueness theorem of a best proximity coupled point. Our results extend and improve many existing results in the literature. Finally, we introduce examples to support our theorems.
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
54E40 | Special maps on metric spaces |
54E50 | Complete metric spaces |