Fixed points of generalized rational \((\alpha,\beta,Z)\)-contraction mappings under simulation functions

Volume 24, Issue 4, pp 345--357 http://dx.doi.org/10.22436/jmcs.024.04.07

Publication Date: April 19, 2021 Submission Date: October 17, 2020 Revision Date: December 26, 2020 Accteptance Date: March 18, 2021

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Authors

Thounaojam Stephen - Department of Mathematics, National Institute of Technology, Manipur, Imphal, 795004, India. Yumnam Rohen - Department of Mathematics, National Institute of Technology, Manipur, Imphal, 795004, India.

Abstract

In this paper, we combine the \((\alpha,\beta)\)-admissible mappings and simulation function in order to obtain the generalized form of rational \((\alpha,\beta,Z)\)-contraction mapping. Further this concept is used in the setting of \(b\)-metric space in order to obtain some fixed point theorems. Suitable examples are also established to verify the validity of the results obtained.

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Keywords

• Fixed points
• generalized rational \((\alpha,\beta,Z)\)-contraction mapping
• \((\alpha,\beta)\)-admissible mappings
• simulation function
• \(b\)-metric space

MSC

•  47H10
•  54H25

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