Huang, Long-Guang; Zhang, Xian Cone metric spaces and fixed point theorems of contractive mappings. (English) Zbl 1118.54022 J. Math. Anal. Appl. 332, No. 2, 1468-1476 (2007). 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 \(d\). Reviewer: Mirosława Zima (Rzeszow) Cited in 94 ReviewsCited in 472 Documents 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 Keywords:cone metric space; fixed point; contractive mapping; ordered Banach space PDF BibTeX XML Cite \textit{L.-G. Huang} and \textit{X. Zhang}, J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022) Full Text: DOI OpenURL 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 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.