Tripled fixed point theorems in cone metric spaces under \(F\)-invariant set and \(c\)-distance

Volume 8, Issue 5, pp 750--762 http://dx.doi.org/10.22436/jnsa.008.05.26

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Authors

Sahar Mohammad Abusalim - School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia. Mohd Salmi Md Noorani - School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia.

Abstract

The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of \(F\)-invariant sets denoted by \(M\) in case of \(M \in X^6\) in cone and ordered cone version. we also establish some tripled fixed point theorems in cone metric spaces under the concept of an \(F\)-invariant set for mappings \(F : X^3 \rightarrow X\) and \(c\)-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.

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Keywords

• Cone metric spaces
• partially ordered cone metric spaces
• tripled fixed points
• c-distance
• F-invariant set.

MSC

•  54H25

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