Common Fixed-Point Theorems and Applications in Complex Valued b- Metric Spaces

Sanjay Kumar; Akash Singhal; Manish Sharma

doi:10.17485/IJST/v16i31.505

Article

Common Fixed-Point Theorems and Applications in Complex Valued b- Metric Spaces

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i31.505

Year: 2023, Volume: 16, Issue: 31, Pages: 2419-2424

Original Article

Common Fixed-Point Theorems and Applications in Complex Valued b- Metric Spaces

Sanjay Kumar^1*, Akash Singhal², Manish Sharma²

¹Research Scholar Department of Mathematics, ITM University, Gwalior, India
²Department of Mathematics, ITM University, Gwalior, India

*Corresponding Author
Email: [email protected]

Received Date:06 March 2023, Accepted Date:06 June 2023, Published Date:16 August 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: The purpose of this paper is to prove some common fixed-point theorems satisfying the rational type of contractive condition in the frame work of complex valued b metric spaces. Methodology: Some well-known common fixed-point result we studied in the complex valued b –metric spaces and replaced the constant of contractive condition by some control function to obtain the new common fixed point theorems and also proving the uniqueness of fixed point for a pair of mappings. Findings: Results based on common fixed point theorems are derived in the context of complex valued –b metric spaces for improved rational inequality, which was the version of the result of Aiman A Mukheimer(1), with an application which shows the applicability and validity of our main result. Novelty: This study revealed the Common fixed-point theorems by replacing the constant of contraction through control function, with suitable application.

Keywords: Common fixed point; Partial order; Cauchy sequence; ComplexValued b metric space; weakly compatible mappings

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Copyright

© 2023 Kumar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)