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Coupled fixed point theorems in quasimetric spaces without mixed monotonicity. (English) Zbl 1474.54217

Summary: In this paper, using the concepts of \(f\)-closed set and inverse \(f\)-closed set, we will prove some fixed point theorems for graphic contractions in complete quasimetric space. Then, as applications, coupled fixed point theorems in quasimetric spaces without the mixed monotonicity property are obtained.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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