Double controlled $ M $-metric spaces and some fixed point results

Fahim Uddin; Faizan Adeel; Khalil Javed; Choonkil Park; Muhammad Arshad; Fahim Uddin; Faizan Adeel; Khalil Javed; Choonkil Park; Muhammad Arshad

doi:10.3934/math.2022838

AIMS Mathematics

2022, Volume 7, Issue 8: 15298-15312. doi: 10.3934/math.2022838

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Research article

Double controlled $ M $-metric spaces and some fixed point results

1.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan
2.
Department of Mathematics and Statistic, International Islamic University, Islamabad, Pakistan
3.
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea

Received: 02 April 2022 Revised: 07 June 2022 Accepted: 13 June 2022 Published: 17 June 2022
MSC : 47H10, 54H25

In this article, we introduce the idea of double controlled $ M $-metric space by employing two control functions $ a(u, w) $ and $ \beta (w, v) $ on the right-hand side of the triangle inequality of $ M $-metric space. We provide some examples of double controlled $ M $-metric spaces. We also provide some fixed point results under new type of contractions in the setting of double controlled $ M $-metric spaces. Moreover, we give an example to highlight the importance of one of our main results.
- fixed point,
- Fredholm integral equation,
- double controlled $ M $-metric space
Citation: Fahim Uddin, Faizan Adeel, Khalil Javed, Choonkil Park, Muhammad Arshad. Double controlled $ M $-metric spaces and some fixed point results[J]. AIMS Mathematics, 2022, 7(8): 15298-15312. doi: 10.3934/math.2022838

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Abstract

In this article, we introduce the idea of double controlled $ M $-metric space by employing two control functions $ a(u, w) $ and $ \beta (w, v) $ on the right-hand side of the triangle inequality of $ M $-metric space. We provide some examples of double controlled $ M $-metric spaces. We also provide some fixed point results under new type of contractions in the setting of double controlled $ M $-metric spaces. Moreover, we give an example to highlight the importance of one of our main results.

References

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