TY - JOUR

T1 - Suzuki’s type characterizations of completeness for partial metric spacesand fixed points for partially ordered metric spaces

AU - Vetro, Pasquale

PY - 2012

Y1 - 2012

N2 - 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 resultson 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 offixed point theory. This result extends Suzuki’s characterization of metric completeness.

AB - 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 resultson 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 offixed point theory. This result extends Suzuki’s characterization of metric completeness.

KW - Common fixed points

KW - Fixed points

KW - Partial metric completeness

KW - Partial metric spaces

KW - Partially ordered metric spaces

KW - Common fixed points

KW - Fixed points

KW - Partial metric completeness

KW - Partial metric spaces

KW - Partially ordered metric spaces

UR - http://hdl.handle.net/10447/61306

M3 - Article

VL - 159

SP - 911

EP - 920

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

ER -