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Fixed point and coupled fixed point theorems on \(b\)-metric-like spaces. (English) Zbl 06275443
Summary: We first introduce the concept of \(b\)-metric-like space which generalizes the notions of partial metric space, metric-like space and \(b\)-metric space. Then we establish the existence and uniqueness of fixed points in a \(b\)-metric-like space as well as in a partially ordered \(b\)-metric-like space. As an application, we derive some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces and \(b\)-metric spaces. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results.

MSC:
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
55M20 Fixed points and coincidences in algebraic topology
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