Fixed point theorems of multi-valued and single-valued mappings in partial metric spaces

Abstract

Matthews (1994) introduced the concept of nonzero self-distance called a partial metric and extended the Banach contraction principle in the context of partial metrics paces. This was followed by Aydi et al. (2012) by extending Nadler’s fixed point theorem to partial metric spaces and introducing the concept of partial Hausdorff metric. In this paper, we prove some fixed point theorems in the context of partial metric spaces endowed with partial ordering using partial Hausdorff metric and a notion of monotone multivalued mappings. Moreover, an example is provided to illustrate the usability of our results.