Common Fixed Points in a Partially Ordered Partial Metric Space

Abstract

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.

Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces

“…The mappings , are said to be weakly compatible if they commute at their coincidence point (i.e., = whenever = ). If ⪯ is a partial order on , then the mapping is calleddominated if ⪯ for all ∈ ; see [23].…”

Fixed point theorems for α−β−ψ -contractive mappings in partially ordered sets

“…The existence of fixed point in partially ordered sets has been considered in [1,2,3,5,6,7,8,9,11,12,15,16,19]. Furthermore, some applications to periodic boundary value problems and matrix equations were given in [13,14,17].…”

On fixed points for for alpha–eta–psi-contractive multi-valued mappings in partial metric spaces

“…On the other hand, Matthews [16] introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context (see also [2,3,10,13,19,20,27]). In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory (see, [9,14,16,23,25,28]).…”