Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

By Daniela Paesano, Pasquale Vetro. 2012

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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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e9a17e5f18bc3d1cd47b137ba72b618358e6cc09

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In Geometry and Topology

1. A. Nastasi
2. Pasquale Vetro
3. E. Karapınar
4. Calogero Vetro

Citations in the corpus

• Fixed point results on metric and partial metric spaces via simulation functions (2015, background): “In this section we recall some definitions and some properties of partial metric spaces that can be found in [12, 13, 14, 15, 16].”