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 selfmapping 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 Rodríguez-López [J.J. Nieto, R. Rodríguez-López, 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 Suzuki’s characterization of metric completeness.

Paesano, D., Vetro, P. (2012). Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. TOPOLOGY AND ITS APPLICATIONS, 159(3), 911-920 [10.1016/j.topol.2011.12.008].

Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

VETRO, Pasquale
2012-01-01

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 selfmapping 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 Rodríguez-López [J.J. Nieto, R. Rodríguez-López, 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 Suzuki’s characterization of metric completeness.
2012
Settore MAT/05 - Analisi Matematica
Paesano, D., Vetro, P. (2012). Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. TOPOLOGY AND ITS APPLICATIONS, 159(3), 911-920 [10.1016/j.topol.2011.12.008].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/61306
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