Partial Hausdorff metric and Nadlerʼs fixed point theorem on partial metric spaces

Common fixed points for multivalued generalized contractions on partial metric spaces

“…If we take T = S in Theorem 2.2, then we obtain the following corollary which generalizes Theorem 3.1 of [8].…”

“…Many authors followed his idea and gave their contributions in that sense, see for example [5][6][7]9,10,16,17,24,25,28,32]. Recently, Aydi, Abbas and Vetro [8] introduced the concept of a partial Hausdorff metric and extended the well known Nadler's fixed point theorem to such spaces.…”

Fixed point theorem for generalized set-valued contractions on partial metric space

“…Recently, Aydi et al [4,2013] introduced the concept of a partial Hausdorff metric and extended the Nadler's fixed point theorem on partial metric spaces using the partial Hausdorff metric.…”

“…It is proved in [4], that e p satisfies the following properties: Consider now the partial Hausdorff metric of A and B defined in [4] which is given by …”

“…This remarkable paper of Mathews constructed another important bridge between the domain theory in computer sciences and fixed point theory in mathematics (see [40]). Later on, many researchers studied fixed point theorems in partial metric spaces, particularly Oltra-Valero [36,2004], Rus [39,2008],Ćirić et al [15,2011], Romaguera [38,2012], Aydi et al [4,2012].…”