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Zbl 1118.54022
Huang, Long-Guang; Zhang, Xian
Cone metric spaces and fixed point theorems of contractive mappings. (English)
[J] J. Math. Anal. Appl. 332, No. 2, 1468-1476 (2007). ISSN 0022-247X

The authors introduce the notion of a cone metric space $(X,d)$. In the classical definition of a metric space they replace the set of real numbers by a Banach space $E$ ordered by a solid cone $P$. They discuss properties of cone metric spaces and prove some fixed point theorems for mappings satisfying contractive conditions with respect to a cone metric $d$.
[Mirosława Zima (Rzeszow)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
54F05 Ordered topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54E35 Metric spaces, metrizability

Keywords: cone metric space; fixed point; contractive mapping; ordered Banach space

Cited in: Zbl 1260.54066 Zbl 1259.54018 Zbl 1252.47081 Zbl 1241.54029 Zbl pre06129370 Zbl 1243.54075 Zbl 1235.54021 Zbl 1235.54036 Zbl 1235.54046 Zbl 1233.54015 Zbl 1233.54020 Zbl 1232.54037 Zbl 1230.54042 Zbl 1230.54048 Zbl 1229.54033 Zbl 1226.54043 Zbl 1223.54053 Zbl 1221.54048 Zbl 1221.54054 Zbl 1220.54031 Zbl 1220.54017 Zbl 1218.54030 Zbl 1206.54058 Zbl 1206.54067 Zbl pre06107672 Zbl pre06096971 Zbl pre06073281 Zbl 1243.54066 Zbl 1242.54029 Zbl 1239.54024 Zbl 1235.54020 Zbl 1220.54020 Zbl 1218.54029 Zbl 1217.54036 Zbl 1210.54054 Zbl 1203.54034 Zbl 1198.54075 Zbl 1198.46014 Zbl 1220.54035 Zbl 1203.54043 Zbl 1203.54042 Zbl 1197.54051 Zbl 1190.54032 Zbl 1189.54036 Zbl 1186.54035 Zbl 1184.54038 Zbl 1179.54060 Zbl 1171.54033 Zbl 1169.54023 Zbl 1167.54014 Zbl 1156.54023 Zbl 1145.54045 Zbl 1196.54086

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