Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces

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. © 2012 Elsevier B.V.