Fixed point theory in complex valued controlled metric spaces with an application

Muhammad Suhail Aslam; Mohammad Showkat Rahim Chowdhury; Liliana Guran; Manar A. Alqudah; Thabet Abdeljawad; Muhammad Suhail Aslam; Mohammad Showkat Rahim Chowdhury; Liliana Guran; Manar A. Alqudah; Thabet Abdeljawad

doi:10.3934/math.2022663

AIMS Mathematics

2022, Volume 7, Issue 7: 11879-11904. doi: 10.3934/math.2022663

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Research article

Fixed point theory in complex valued controlled metric spaces with an application

1.
Department of Mathematics and Statistics, Faculty of Science, University of Lahore, Lahore, Pakistan
2.
Department of Pharmaceutical Sciences, "Vasile Goldiş" Western University of Arad, Arad, L. Rebreanu Street, No. 86, 310048, Romania
3.
Department Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O.Box 84428, Riyadh 11671, Saudi Arabia
4.
Department of Mathematics and Sciences, Prince Sultan University, P.O.Box 66833, Riyadh 11586, Saudi Arabia
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 21 December 2021 Revised: 09 April 2022 Accepted: 12 April 2022 Published: 20 April 2022
MSC : 24H25, 47H09, 47H10

In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b $-metric type space and this one is different from complex valued extended $ b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.
- complex valued controlled,
- metric type spaces,
- complex valued metrics types,
- unique fixed point,
- Bannach contraction,
- integral equation
Citation: Muhammad Suhail Aslam, Mohammad Showkat Rahim Chowdhury, Liliana Guran, Manar A. Alqudah, Thabet Abdeljawad. Fixed point theory in complex valued controlled metric spaces with an application[J]. AIMS Mathematics, 2022, 7(7): 11879-11904. doi: 10.3934/math.2022663

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Abstract

In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b $-metric type space and this one is different from complex valued extended $ b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.

References

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