Some Common Fixed Point Results in Cone Metric Spaces

By Muhammad Arshad, Akbar Azam, Pasquale Vetro. 2009

147 citations recorded by the source corpus.

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/afbf7b5f49285bb9ca7d96bcf818c005ea08cc16

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In Geometry and Topology

Citations in the corpus

Multi-valued F-contractions and the solutions of certain functional and integral equations (2013, background): “Starting from these considerations, the study of fixed and common fixed points of mappings satisfying a certain metrical contractive condition attracted many researchers, see for example [3, 4, 6, 11, 14, 15, 21, 23–28].”
On cone metric spaces: A survey (2011, unknown): “1 and the approach in all the papers [55–83], where the only assumption on the cone is that it has a nonempty interior, show how to obtain results without using continuity of the metric and Sandwich Theorem.”
Fixed Point Results for F-Contractive Mappings of Hardy-Rogers-Type (2014, background): “Starting from these considerations, the study of fixed and common fixed points of mappings satisfying a certain metrical contractive condition attracted many researchers, see for example [1–3, 5, 6, 8–11, 16, 22–27].”
Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications (2013, background): “[4], Azam and Arshad [5], Latif and Shaddad [6], Karapınar [7], and many others obtained fixed point theorems in cone metric spaces (see [8]).”