On the Perov's type $ (\beta, F) $-contraction principle and an application to delay integro-differential problem

Muhammad Nazam; Hijaz Ahmad; Muhammad Waheed; Sameh Askar; Muhammad Nazam; Hijaz Ahmad; Muhammad Waheed; Sameh Askar

doi:10.3934/math.20231217

AIMS Mathematics

2023, Volume 8, Issue 10: 23871-23888. doi: 10.3934/math.20231217

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Research article

On the Perov's type $ (\beta, F) $-contraction principle and an application to delay integro-differential problem

1.
Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan
2.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
3.
Near East University, Operational Research Center in Healthcare, Nicosia, PC: 99138, TRNC Mersin 10, Turkey
4.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
5.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 28 April 2023 Revised: 14 June 2023 Accepted: 04 July 2023 Published: 07 August 2023
MSC : 45J05, 47H10, 54H25

We present Perov's type $ (\beta, F) $-contraction principle and examine the fixed points of the self-operators satisfying Perov's type $ (\beta, F) $-contraction principle in the context of vector-valued $ b $-metrics. A specific instance of the $ (\beta, F) $-contraction principle is the $ F $-contraction principle. We generalize a number of recent findings that are already in the literature and provide an example to illustrate the hypothesis of the main theorem. We apply the obtained fixed point theorem to show the existence of the solution to the delay integro-differential problem.
- fixed point,
- Perov's type $ (\beta, F) $-contraction operator,
- $ \beta $-complete vector-valued $ b $-metric space
Citation: Muhammad Nazam, Hijaz Ahmad, Muhammad Waheed, Sameh Askar. On the Perov's type $ (\beta, F) $-contraction principle and an application to delay integro-differential problem[J]. AIMS Mathematics, 2023, 8(10): 23871-23888. doi: 10.3934/math.20231217

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Abstract

We present Perov's type $ (\beta, F) $-contraction principle and examine the fixed points of the self-operators satisfying Perov's type $ (\beta, F) $-contraction principle in the context of vector-valued $ b $-metrics. A specific instance of the $ (\beta, F) $-contraction principle is the $ F $-contraction principle. We generalize a number of recent findings that are already in the literature and provide an example to illustrate the hypothesis of the main theorem. We apply the obtained fixed point theorem to show the existence of the solution to the delay integro-differential problem.

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