Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces. (English) Zbl 1252.54027

Summary: We introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. Moreover, we give a homotopy result as application of our main result.


54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
54C60 Set-valued maps in general topology
Full Text: DOI


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