Strong convergence to fixed points of an evolution subfamily

Gul Rahmat; Tariq Shah; Muhammad Sarwar; Saber Mansour; Hassen Aydi; Gul Rahmat; Tariq Shah; Muhammad Sarwar; Saber Mansour; Hassen Aydi

doi:10.3934/math.20231039

AIMS Mathematics

2023, Volume 8, Issue 9: 20380-20394. doi: 10.3934/math.20231039

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Research article

Strong convergence to fixed points of an evolution subfamily

1.
Department of Mathematics, Islamia College University Peshawar, Peshawar, Pakistan; gulrahmat@icp.edu.pk; tariqshahmaths@gmail.com
2.
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
3.
Department of Mathematics, Umm Al-Qura University, Faculty of Applied sciences, P. O. Box 14035, Holly Makkah 21955, Saudi Arabia; samansour@uqu.edu.sa
4.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
5.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 06 February 2023 Revised: 27 April 2023 Accepted: 03 May 2023 Published: 21 June 2023
MSC : 34A08, 47H10, 54H25

In this manuscript, we give strong convergence results for a fixed point of a subfamily of an evolution family on a convex and closed subset $ \mathcal{D} $ of a Banach space $ \mathsf{B} $. An example is also provided which shows the applications of evolution families and our main results. At the end, an open problem is given.
- non-expansive mappings,
- strong convergence,
- evolution family,
- Banach space
Citation: Gul Rahmat, Tariq Shah, Muhammad Sarwar, Saber Mansour, Hassen Aydi. Strong convergence to fixed points of an evolution subfamily[J]. AIMS Mathematics, 2023, 8(9): 20380-20394. doi: 10.3934/math.20231039

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Abstract

In this manuscript, we give strong convergence results for a fixed point of a subfamily of an evolution family on a convex and closed subset $ \mathcal{D} $ of a Banach space $ \mathsf{B} $. An example is also provided which shows the applications of evolution families and our main results. At the end, an open problem is given.

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