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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.

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
55M20 Fixed points and coincidences in algebraic topology
Full Text: DOI
[1] doi:10.1016/j.na.2010.06.084 · Zbl 1321.54085 · doi:10.1016/j.na.2010.06.084
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[6] doi:10.1016/j.na.2011.10.014 · Zbl 1242.54027 · doi:10.1016/j.na.2011.10.014
[7] doi:10.1016/j.aml.2011.02.004 · Zbl 1214.54033 · doi:10.1016/j.aml.2011.02.004
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