Cone metric spaces and fixed point theorems of contractive mappings

By Long Huang, Xian Zhang. 2007

1,595 citations recorded by the source corpus.

In this paper we introduce cone metric spaces, prove some fixed point theorems of contractive mappings on cone metric spaces.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0a7919840dc18fe1007f83dd740d9f01365bbf47

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In Geometry and Topology

Citations in the corpus

Coupled fixed point, $F$-invariant set and fixed point of $N$-order (2010, background): “Concerning the definitions and properties of cone metric spaces, the reader can refer to Huang and Zhang [12].”
Fixed points of weak contractions in cone metric spaces (2010, background): “1 ([13]).”
Cone metric spaces and fixed point theorems of T-Kannan contractive mappings (2009, methodology): “Our results generalize the respective theorems given in [3] and [4].”
THE EQUIVALENCE OF CONE METRIC SPACES AND METRIC SPACES (2010, background): “Consistent with Huang and Zhang [6], the following definitions and results will be needed in the sequel.”
Some Common Coupled Fixed Point Results in Cone Metric Spaces (2010, background): “For a survey of coincidence point theory over cone metric spaces, we refer the reader (as examples) to [1-4,6-14].”
A fixed point theorem for set-valued quasi-contractions in b-metric spaces (2012, neutral): “Notice that in [[14], Lemma 5], if the cone P is normal with a constant K, then the cone metric d : X × X ® E is continuous, i.”
Generalized common fixed point theorems in complex valued metric spaces and applications (2012, background): “Many authors generalized and extended the notion of a metric spaces such as a vector-valued metric spaces of Perov [20], a G-metric spaces of Mustafa and Sims [21], a cone metric spaces of Huang and Zhang [22], a modular metric spaces of Chistyakov [23], and etc.”
Cone metric spaces and fixed point theorems in diametrically contractive mappings (2010, methodology): “Theorem 1 [ 1 ] Let (X, d) be a complete cone metric space, P be a normal cone with normal”
Some Equivalences between Cone $b$-Metric Spaces and $b$-Metric Spaces (2013, background): “Note that the relation between a cone b-metric and a bmetric is likely the relation between a cone metric [11] and a metric.”
On cone metric spaces: A survey (2011, background): “Let us mention [1] that if P is a normal solid cone, then {xn} is a Cauchy sequence if and only if ‖d(xn, xm)‖ → 0, n,m → ∞.”