6533b82ffe1ef96bd1295b34
RESEARCH PRODUCT
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces
Daniela PaesanoPasquale Vetrosubject
Discrete mathematicsPartial metric spacesPartially ordered metric spacesInjective metric spaceMathematics::General TopologyPartial metric completenessEquivalence of metricsFixed-point propertyFixed points Common fixed points Partial metric spaces Partially ordered metric spaces Partial metric completenessConvex metric spaceIntrinsic metricLeast fixed pointFixed pointsMetric spaceSettore MAT/05 - Analisi MatematicaCommon fixed pointsGeometry and TopologyMetric differentialMathematicsdescription
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435–1443], Nieto and Rodriguez-Lopez [J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239]. We deduce, also, common fixed point results for two self-mappings. Moreover, using our results, we obtain a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends Suzukiʼs characterization of metric completeness.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-02-01 | Topology and its Applications |