Rational interpolative contractions with applications in extended $ b $-metric spaces

Muhammad Sarwar; Muhammad Fawad; Muhammad Rashid; Zoran D. Mitrović; Qian-Qian Zhang; Nabil Mlaiki; Muhammad Sarwar; Muhammad Fawad; Muhammad Rashid; Zoran D. Mitrović; Qian-Qian Zhang; Nabil Mlaiki

doi:10.3934/math.2024683

AIMS Mathematics

2024, Volume 9, Issue 6: 14043-14061. doi: 10.3934/math.2024683

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Research article

Rational interpolative contractions with applications in extended $ b $-metric spaces

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L) 18000, Khyber Pakhtunkhwa, Pakistan; sarwar@uom.edu.pk, muhmmadfawad123@gmail.com, mrashidghani26@gmail.com
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; nmlaiki@psu.edu.sa
3.
Faculty of Electrical Engineering, University of Banja Luka, Patre 5, Banja Luka 78000, Bosnia and Herzegovina; zoran.mitrovic@etf.unibl.org
4.
College of Science, Northwest A&F University, Yangling 712100, China; zhangqq2019@nwafu.edu.cn

Received: 03 February 2024 Revised: 01 April 2024 Accepted: 10 April 2024 Published: 18 April 2024
MSC : 45E99, 47H10, 54H25, 55M20

In this manuscript, utilizing interpolative contractions with fractional forms, some unique fixed-point results were studied in the context of extended $ b $-metric spaces. For the validity of the presented results some examples are given. In the last section an existence theorem is provided to study the existence of a solution for the Fredholm integral equation.
- fixed point,
- metric space,
- interpolative contractions,
- extended $ b $-metric space,
- integral equation
Citation: Muhammad Sarwar, Muhammad Fawad, Muhammad Rashid, Zoran D. Mitrović, Qian-Qian Zhang, Nabil Mlaiki. Rational interpolative contractions with applications in extended $ b $-metric spaces[J]. AIMS Mathematics, 2024, 9(6): 14043-14061. doi: 10.3934/math.2024683

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Abstract

In this manuscript, utilizing interpolative contractions with fractional forms, some unique fixed-point results were studied in the context of extended $ b $-metric spaces. For the validity of the presented results some examples are given. In the last section an existence theorem is provided to study the existence of a solution for the Fredholm integral equation.

References

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