Common fixed point theorems for multi-valued mappings in bicomplex valued metric spaces with application

Afrah Ahmad Noman Abdou; Afrah Ahmad Noman Abdou

doi:10.3934/math.20231027

AIMS Mathematics

2023, Volume 8, Issue 9: 20154-20168. doi: 10.3934/math.20231027

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Research article

Common fixed point theorems for multi-valued mappings in bicomplex valued metric spaces with application

Afrah Ahmad Noman Abdou ^,

Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 10 March 2023 Revised: 03 June 2023 Accepted: 06 June 2023 Published: 19 June 2023
MSC : 46S40, 47H10, 54H25

The aim of this article is to introduce a generalized Hausdorff distance function in the setting of a bicomplex valued metric space. Using this, we obtain common fixed point theorems for generalized contractions. Our outcomes extend and generalize some conventional fixed point results in the literature. We also furnish a significant example to express the genuineness of the presented results. As an application, we derive some common fixed point results for self mappings, including the leading results of [Demonstr. Math., 54 (2021), 474-487] and [Int. J. Nonlinear Anal. Appl., 12 (2021), 717-727].
- common fixed point,
- multi-valued mappings,
- bicomplex valued metric space,
- generalized Hausdorff distance function
Citation: Afrah Ahmad Noman Abdou. Common fixed point theorems for multi-valued mappings in bicomplex valued metric spaces with application[J]. AIMS Mathematics, 2023, 8(9): 20154-20168. doi: 10.3934/math.20231027

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Abstract

The aim of this article is to introduce a generalized Hausdorff distance function in the setting of a bicomplex valued metric space. Using this, we obtain common fixed point theorems for generalized contractions. Our outcomes extend and generalize some conventional fixed point results in the literature. We also furnish a significant example to express the genuineness of the presented results. As an application, we derive some common fixed point results for self mappings, including the leading results of [Demonstr. Math., 54 (2021), 474-487] and [Int. J. Nonlinear Anal. Appl., 12 (2021), 717-727].

References

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