Abstract
Abstract Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. Examples are provided when these results can be applied and neither corresponding metric results nor the results with the standard completeness assumption of the underlying partial metric space can. MSC:47H10, 54H25.
Highlights
1 Introduction and preliminaries Matthews [ ] introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks. He showed that the Banach contraction mapping theorem can be generalized to the partial metric context for applications in program verification
We prove in Section a common fixed point theorem for g-quasicontractions in -complete spaces that contains as special cases several other results
In Section we deduce a partial metric version of fixed point theorem under the condition [, ( )] of B
Summary
Introduction and preliminariesMatthews [ ] introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks. Several authors (see, e.g., [ – , , , – , , , , ]) derived fixed point theorems in partial metric spaces. ] that a partial metric space (X, p) is -complete if and only if every ps-Caristi mapping on X has a fixed point.
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