Remarks on Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings

By Mohamed Amine Khamsi. 2010

176 citations recorded by the source corpus.

We discuss the newly introduced concept of cone metric spaces. We also discuss the fixed point existence results of contractive mappings defined on such metric spaces. In particular, we show that most of the new results are merely copies of the classical ones.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d4fab64606533ea109759f066ca18b7d43bbca3e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

Citations in the corpus

Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces (2014, background): “Recently, Khamsi [15] and Khamsi and Hussain [16] have dealt with spaces of this kind, although under different names (in the spaces called “metric-type”) and obtained (common) fixed point results.”
Various generalizations of metric spaces and fixed point theorems (2015, background): “In particular, relations among bounded 2-metric spaces, metric-type space in the sense of Khamsi [89] and S-metric spaces [130] were stated in [56].”
On relaxations of contraction constants and Caristi’s theorem in b-metric spaces (2016, background): “Khamsi [19] also introduced another definition of a metric type, that was called an s-relaxedp metric in [15, Definition 4.”
On cone metric spaces: A survey (2011, background): “Soon after this work many articles concerned with cone spaces with normal cones appeared (see [9–53]).”