On Geraghty $ \perp $-contractions in $ O $-metric spaces and an application to an ordinary type differential equation

S. S. Razavi; H. P. Masiha; Hüseyin Işık; Hassen Aydi; Choonkil Park; S. S. Razavi; H. P. Masiha; Hüseyin Işık; Hassen Aydi; Choonkil Park

doi:10.3934/math.2022958

AIMS Mathematics

2022, Volume 7, Issue 9: 17393-17402. doi: 10.3934/math.2022958

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Research article

On Geraghty $ \perp $-contractions in $ O $-metric spaces and an application to an ordinary type differential equation

1.
Faculty of Mathematics, K.N. Toosi University of Technology, Tehran, Iran
2.
Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma 10200, Balıkesir, Turkey
3.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, 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.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 13 April 2022 Revised: 29 June 2022 Accepted: 06 July 2022 Published: 27 July 2022
MSC : 39B55, 47H10

By combining the concept of orthogonality and the Geraghty type contraction, we give some fixed point results in the class of $ O $-metric spaces. Our obtained results extend the existing results in the literature. We also resolve an ordinary type differential equation.
- $ O $-metric space,
- Geraghty contraction mapping,
- orthogonal set,
- ordinary differential equation
Citation: S. S. Razavi, H. P. Masiha, Hüseyin Işık, Hassen Aydi, Choonkil Park. On Geraghty $ \perp $-contractions in $ O $-metric spaces and an application to an ordinary type differential equation[J]. AIMS Mathematics, 2022, 7(9): 17393-17402. doi: 10.3934/math.2022958

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Abstract

By combining the concept of orthogonality and the Geraghty type contraction, we give some fixed point results in the class of $ O $-metric spaces. Our obtained results extend the existing results in the literature. We also resolve an ordinary type differential equation.

References

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