Applications and theorem on common fixed point in complex valued b-metric space

Khaled Berrah; Abdelkrim Aliouche; Taki eddine Oussaeif; Khaled Berrah; Abdelkrim Aliouche; Taki eddine Oussaeif

doi:10.3934/math.2019.3.1019

AIMS Mathematics

2019, Volume 4, Issue 3: 1019-1033. doi: 10.3934/math.2019.3.1019

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Research article

Applications and theorem on common fixed point in complex valued b-metric space

1.
Department of Mathematics and Computer and Science, Larbi ben M’hidi University, Oum el Bouaghi, Algeria
2.
Laboratory of mathematics, informatics and systems (LAMIS) Larbi Tebessi university, Tebessa, Algeria

Received: 06 February 2019 Accepted: 18 July 2019 Published: 31 July 2019
MSC : 47H10

In this paper, a common fixed point theorem for four self-mappings satisfying rational contraction has been proved in complex valued b-metric space. Then, examples are provided to verify the effectiveness and usability of our main results. Finally, we validate our results by proving both the existence and the uniqueness of a common solution of the system of Urysohn integral equations and the existence of a unique solution for linear equations system.
- complex valued b-metric space,
- common fixed point,
- compatible mapping,
- weakly compatible mapping,
- integral equations,
- linear system
Citation: Khaled Berrah, Abdelkrim Aliouche, Taki eddine Oussaeif. Applications and theorem on common fixed point in complex valued b-metric space[J]. AIMS Mathematics, 2019, 4(3): 1019-1033. doi: 10.3934/math.2019.3.1019

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Abstract

In this paper, a common fixed point theorem for four self-mappings satisfying rational contraction has been proved in complex valued b-metric space. Then, examples are provided to verify the effectiveness and usability of our main results. Finally, we validate our results by proving both the existence and the uniqueness of a common solution of the system of Urysohn integral equations and the existence of a unique solution for linear equations system.

References

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