A note on cone metric fixed point theory and its equivalence

By Wei-Shih Du. 2010

279 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/46faf576bb7d32a3e4eb71ecfc2e9f7a85e3c8ae

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In Geometry and Topology

Citations in the corpus

Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications (2015, unknown): “Unfortunately, recently these problems became not attractive since some scholars found the equivalence of fixed point results between cone metric spaces and metric spaces, also between cone b-metric spaces and b-metric spaces (see [4, 5, 6, 7, 13, 14]).”
Various generalizations of metric spaces and fixed point theorems (2015, background): “In 2010, Du [51] investigated the equivalence of vectorial versions of fixed point theorems in tvs-cone metric spaces and scalar versions of fixed point theorems in metric spaces as follows.”
Some Equivalences between Cone $b$-Metric Spaces and $b$-Metric Spaces (2013, methodology): “Very recently, Du used the method in [12] to introduce a b-metric on a cone bmetric space and stated some relations between fixed point theorems on cone b-metric spaces and on b-metric spaces [17].”
Fixed point results in generalized metric spaces without Hausdorff property (2014, methodology): “These include, among others, the so-called scalarization method [38] and the method of Minkowski functional [39].”
A Note on Various Types of Cones and Fixed Point Results in Cone Metric Spaces (2013, methodology): “Later, these definitions were extended for tvs-cone valued cone metric spaces in [5] (see also [8, 14]).”
On cone metric spaces: A survey (2011, methodology): “In [84,85] the so-called scalarization functions have been used that had been introduced in the optimization theory, while in [86] properties of basis and dual basis in Banach spaces have been applied.”
Fixed point results under c-distance in tvs-cone metric spaces (2011, methodology): “From [1,5-7], we give the following Definition 1 Let X be a nonempty set and (E, P) an ordered tvs.”
Coupled fixed point, $F$-invariant set and fixed point of $N$-order (2010, background): “In fact in [10], the proof of the above Theorem 3.”