Some generalized fixed point results via a $ \tau $-distance and applications

Farhan Khan; Muhammad Sarwar; Arshad Khan; Muhammad Azeem; Hassen Aydi; Aiman Mukheimer; Farhan Khan; Muhammad Sarwar; Arshad Khan; Muhammad Azeem; Hassen Aydi; Aiman Mukheimer

doi:10.3934/math.2022080

AIMS Mathematics

2022, Volume 7, Issue 1: 1346-1365. doi: 10.3934/math.2022080

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Research article

Some generalized fixed point results via a $ \tau $-distance and applications

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
2.
Department of Statistics, University of Malakand, Chakdara Dir(L), Pakistan
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.
Department of Mathematics and Natural Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 22 February 2021 Accepted: 13 October 2021 Published: 25 October 2021
MSC : Primary 47H10, Secondary 54H25

The aim of this manuscript is to present some new fixed point results in complete partially order metric spaces and to derive some extended forms of Suzuki and Banach fixed point theorems via a $ \tau $-distance by applying some new control functions. Our results are extensions of several existing fixed point theorems in the literature. To show the dominance of the established results, some examples and an application are studied.
- partially ordered metric space,
- complete metric space,
- Banach fixed point theorem,
- Suzuki fixed point theorem,
- $ \omega $-distance,
- $ \tau $-distance
Citation: Farhan Khan, Muhammad Sarwar, Arshad Khan, Muhammad Azeem, Hassen Aydi, Aiman Mukheimer. Some generalized fixed point results via a $ \tau $-distance and applications[J]. AIMS Mathematics, 2022, 7(1): 1346-1365. doi: 10.3934/math.2022080

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Abstract

The aim of this manuscript is to present some new fixed point results in complete partially order metric spaces and to derive some extended forms of Suzuki and Banach fixed point theorems via a $ \tau $-distance by applying some new control functions. Our results are extensions of several existing fixed point theorems in the literature. To show the dominance of the established results, some examples and an application are studied.

References

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