• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

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

Original Article

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

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


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


  1. Bakhtin I. The contraction principle in quasi metric spaces. Functional Analysis. 1989;30:26–37. Available from: https://doi.org/10.4236/oalib.1104657
  2. Azam A, Fisher B, Khan M. Common Fixed Point Theorems in Complex Valued Metric Spaces. Numerical Functional Analysis and Optimization. 2011;32(3):243–253. Available from: https://www.tandfonline.com/doi/abs/10.1080/01630563.2011.533046
  3. Bhatt S, Chaukiyal, Dimri RC. A common fixed point theorem for weakly compatible maps in complex valued metric spaces. International Journal of Mathematical Sciences and Applications. 2011;1(3):1385–1389. Available from: https://ijmsa.yolasite.com/resources/42--sep.pdf
  4. Gnanaprakasam AJ, Boulaaras SM, Mani G, Cherif B, Idris SA. Solving system of linear equations via bicomplex valued metric space. Demonstratio Mathematica. 2021;54(1):474–487. Available from: https://doi.org/10.1515/dema-2021-0046
  5. CPR, A AX, Joseph M, Marudai J. Common fixed point theorems under rational contractions in complex valued extended b-metric spaces. International Journal of Nonlinear Analysis and Applications. 2022;13(1):3479–3490. Available from: https://doi.org/10.22075/IJNAA.2020.20025.2118


© 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)


Subscribe now for latest articles and news.