In this paper, 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.
Aydi, H., Abbas, M., Vetro, C. (2012). Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces. TOPOLOGY AND ITS APPLICATIONS, 159(14), 3234-3242 [10.1016/j.topol.2012.06.012].
Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces
VETRO, Calogero
2012-01-01
Abstract
In this paper, 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.
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