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In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010(2010, Article ID 518243, 10 pages] have studied a new inexact iterative scheme for fixed points of contractive multifunctions. In this paper, using the partial Hausdorff metric introduced by Aydi et al., we prove an analogous to a result of Reich and Zaslavski for contractive multifunctions in the setting of partial metric spaces. An example is given to illustrate our result.2000 AMS Classification: 47H10, 47H09.