# zbMATH — the first resource for mathematics

Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. (English) Zbl 1241.54035
The following two abstract and a little artificial notions are studied: (i) partial metric spaces; (ii) $$0$$-complete metric spaces.
Then some formal generalizations of the Banach contraction theorem for mappings in such spaces are obtained. Moreover, a coincidence result is proved.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems
Full Text:
##### References:
 [1] Altun, I.; Durmaz, G., Some fixed point theorems on ordered cone metric spaces, Rend. circ. mat. Palermo, 58, 319-325, (2009) · Zbl 1184.54038 [2] Haghi, R.H.; Rezapour, Sh.; Shahzad, N., Some fixed point generalizations are not real generalizations, Nonlinear anal., 74, 1799-1803, (2011) · Zbl 1251.54045 [3] Kirk, W.A., Caristiʼs fixed point theorem and metric convexity, Colloq. math., 36, 81-86, (1976) · Zbl 0353.53041 [4] Matthews, S.G., Partial metric topology, (), 183-197 · Zbl 0911.54025 [5] Nieto, J.J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013 [6] OʼNeill, S.J., Partial metrics, valuations and domain theory, (), 304-315 · Zbl 0889.54018 [7] Oltra, S.; Valero, O., Banachʼs fixed point theorem for partial metric spaces, Rend. istit. mat. univ. trieste, 36, 17-26, (2004) · Zbl 1080.54030 [8] Ran, A.C.M.; Reurings, M.C., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. amer. math. soc., 132, 1435-1443, (2004) · Zbl 1060.47056 [9] Romaguera, S., A kirk type characterization of completeness for partial metric spaces, Fixed point theory appl., 2010, (2010), Article ID 493298, 6 pp · Zbl 1193.54047 [10] Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. amer. math. soc., 136, 1861-1869, (2008) · Zbl 1145.54026 [11] Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. gen. topol., 6, 229-240, (2005) · Zbl 1087.54020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.