\(N\) fixed point theorems and \(N\) best proximity point theorems for generalized contraction in partially ordered metric spaces. (English) Zbl 1489.54255
Summary: The purpose of this paper is to prove the \(n\) fixed point theorems and \(n\) best proximity point theorems for generalized contraction in partially ordered metric spaces. We firstly investigate the \(n\) fixed point theorems. And on this basis, we obtain the \(n\) best proximity point theorems using \(P\)-operator technique. Many recent results in this area have been generalized and improved.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
Keywords:
\(N\) fixed point; \(n\) best proximity point; generalized contraction; weak \(P\)-monotone propertyReferences:
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