Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations

Muhammad Suhail Aslam; Mohammad Showkat Rahim Chowdhury; Liliana Guran; Isra Manzoor; Thabet Abdeljawad; Dania Santina; Nabil Mlaiki; Muhammad Suhail Aslam; Mohammad Showkat Rahim Chowdhury; Liliana Guran; Isra Manzoor; Thabet Abdeljawad; Dania Santina; Nabil Mlaiki

doi:10.3934/math.2023247

AIMS Mathematics

2023, Volume 8, Issue 2: 4944-4963. doi: 10.3934/math.2023247

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Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations

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 310048, Romania
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudia Arabia

Received: 30 September 2022 Revised: 29 November 2022 Accepted: 05 December 2022 Published: 09 December 2022
MSC : 47H10, 54H25

In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results.
- fixed point,
- complex-valued double controlled metric like spaces,
- Fredholm type integral equations
Citation: Muhammad Suhail Aslam, Mohammad Showkat Rahim Chowdhury, Liliana Guran, Isra Manzoor, Thabet Abdeljawad, Dania Santina, Nabil Mlaiki. Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations[J]. AIMS Mathematics, 2023, 8(2): 4944-4963. doi: 10.3934/math.2023247

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Abstract

In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results.

References

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