Rational contractions on complex-valued extended $ b $-metric spaces and an application

Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei; Hassen Aydi; Manuel De La Sen; Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei; Hassen Aydi; Manuel De La Sen

doi:10.3934/math.2023172

AIMS Mathematics

2023, Volume 8, Issue 2: 3338-3352. doi: 10.3934/math.2023172

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Research article

Rational contractions on complex-valued extended $ b $-metric spaces and an application

1.
Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
4.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
6.
Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country Campus of Leioa, Leioa (Bizkaia) 48940, Spain

Received: 22 September 2022 Revised: 30 October 2022 Accepted: 09 November 2022 Published: 17 November 2022
MSC : 46S40, 47H10, 54H25

The aim of this article is to obtain common fixed point results on complex-valued extended $ b $-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended $ b $-metric spaces.
- complex-valued extended $ b $-metric space,
- common fixed point,
- control functions,
- rational expressions
Citation: Jamshaid Ahmad, Abdullah Eqal Al-Mazrooei, Hassen Aydi, Manuel De La Sen. Rational contractions on complex-valued extended $ b $-metric spaces and an application[J]. AIMS Mathematics, 2023, 8(2): 3338-3352. doi: 10.3934/math.2023172

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Abstract

The aim of this article is to obtain common fixed point results on complex-valued extended $ b $-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended $ b $-metric spaces.

References

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