Cone \(A_{b}\)-metric space and some coupled fixed point theorems

Volume 24, Issue 3, pp 246--255 http://dx.doi.org/10.22436/jmcs.024.03.06

Publication Date: March 06, 2021 Submission Date: April 10, 2020 Revision Date: January 28, 2021 Accteptance Date: January 29, 2021

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Authors

K. Anthony Singh - Department of Mathematics, D. M. College of Science, Dhanamanjuri University, Imphal (Manipur), India. M. R. Singh - Department of Mathematics, Manipur University, Canchipur (Manipur), India. M. Bina Devi - Department of Mathematics, D. M. College of Science, Dhanamanjuri University, Imphal (Manipur), India. Th. Chhatrajit Singh - Department of Mathematics, Manipur Technical University, Takyelpat (Manipur)-795004, India.

Abstract

In this paper, we extend the definition of coupled fixed point to mappings on cone \(A_{b}\)-metric space and prove some coupled fixed point theorems. Our results extend the coupled fixed point results of Singh and Singh [K. A. Singh, M. R. Singh, J. Math. Comput. Sci., \(\bf 10\) (2020), 891--905] to cone \(A_{b}\)-metric space. An example is also given to illustrate the validity of our result.

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Keywords

• Coupled fixed point
• cone metric space
• cone \(A_{b}\)-metric space

MSC

•  47H10
•  54H25

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