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Set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces. (English) Zbl 1287.54045
Summary: In this paper we introduce set-valued Hardy-Rogers type contractions in 0-complete partial metric spaces and prove the corresponding fixed point theorem. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by H. Aydi et al. [Topology Appl. 159, No. 14, 3234–3242 (2012; Zbl 1252.54027)]. As an application of our results, a homotopy theorem for such mappings is derived. Also, some examples are included which show that our generalization is proper.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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