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Fixed point results for generalized \((\alpha, \psi)\)-contraction mapping in rectangular \(b\)-metric spaces. (English) Zbl 1502.54044

Summary: In this paper, we introduce generalized \(( \alpha , \psi)\)-contraction mappings in the setting of rectangular \(b\)-metric spaces and establish existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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