Best proximity point of $ \alpha $-$ \eta $-type generalized $ F $-proximal contractions in modular metric spaces

Yao Yu; Chaobo Li; Dong Ji; Yao Yu; Chaobo Li; Dong Ji

doi:10.3934/math.2024436

AIMS Mathematics

2024, Volume 9, Issue 4: 8940-8960. doi: 10.3934/math.2024436

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Research article

Best proximity point of $ \alpha $-$ \eta $-type generalized $ F $-proximal contractions in modular metric spaces

Yao Yu ¹,
Chaobo Li ^{2
,
,},
Dong Ji ^1,2

1.
Department of Mathematics, Harbin University, Harbin 150086, China
2.
Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

Received: 20 December 2023 Revised: 16 February 2024 Accepted: 22 February 2024 Published: 04 March 2024
MSC : 47H10, 54H25

The purpose of this paper is to present a study of $ \alpha $-$ \eta $-type generalized $ F $-proximal contraction mappings in the framework of modular metric spaces and to prove some best proximity point theorems for these types of mappings. Some examples are given to show the validity of our results. We also apply our results to establish the existence of solutions for a certain type of non-linear integral equation.
- best proximity point,
- modular metric space,
- generalized $ F $-proximal contractions,
- uniform approximation
Citation: Yao Yu, Chaobo Li, Dong Ji. Best proximity point of $ \alpha $-$ \eta $-type generalized $ F $-proximal contractions in modular metric spaces[J]. AIMS Mathematics, 2024, 9(4): 8940-8960. doi: 10.3934/math.2024436

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Abstract

The purpose of this paper is to present a study of $ \alpha $-$ \eta $-type generalized $ F $-proximal contraction mappings in the framework of modular metric spaces and to prove some best proximity point theorems for these types of mappings. Some examples are given to show the validity of our results. We also apply our results to establish the existence of solutions for a certain type of non-linear integral equation.

References

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