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Cone metric spaces and fixed point theorems of contractive mappings. (English) Zbl 1118.54022
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 \(d\).

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
54E35 Metric spaces, metrizability
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References:
[1] Deimling, K., Nonlinear functional analysis, (1985), Springer-Verlag · Zbl 0559.47040
[2] Rhoades, B.E., A comparison of various definition of contractive mappings, Trans. amer. math. soc., 266, 257-290, (1977) · Zbl 0365.54023
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