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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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