Iterative approximation of fixed points of generalized $ \alpha _{m} $-nonexpansive mappings in modular spaces

Muhammad Waseem Asghar; Mujahid Abbas; Cyril Dennis Enyi; McSylvester Ejighikeme Omaba; Muhammad Waseem Asghar; Mujahid Abbas; Cyril Dennis Enyi; McSylvester Ejighikeme Omaba

doi:10.3934/math.20231378

AIMS Mathematics

2023, Volume 8, Issue 11: 26922-26944. doi: 10.3934/math.20231378

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Iterative approximation of fixed points of generalized $ \alpha _{m} $-nonexpansive mappings in modular spaces

1.
Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
2.
Department of Medical Research, China Medical Unversity, Taichung 404, Taiwan
3.
Department of Mathematics, University of Hafr Al Batin, Saudi Arabia

Received: 15 July 2023 Revised: 05 September 2023 Accepted: 10 September 2023 Published: 21 September 2023
MSC : 37C25, 47H09, 47H10

Our aim of this work is to approximate the fixed points of generalized $ \alpha _{m} $-nonexpansive mappings employing $ AA $-iterative scheme in the structure of modular spaces. The results of fixed points for generalized $ \alpha _{m} $-nonexpansive mappings is proven in this context. Moreover, the stability of the scheme and data dependence results are given for $ m $-contraction mappings. In order to demonstrate that the $ AA $-iterative scheme converges faster than some other schemes for generalized $ \alpha_{m} $-nonexpansive mappings, numerical examples are shown at the end.
- fixed point,
- $ AA $-Iteration,
- modular space,
- generalized $ \alpha_{m} $-nonexpansive mapping
Citation: Muhammad Waseem Asghar, Mujahid Abbas, Cyril Dennis Enyi, McSylvester Ejighikeme Omaba. Iterative approximation of fixed points of generalized $ \alpha _{m} $-nonexpansive mappings in modular spaces[J]. AIMS Mathematics, 2023, 8(11): 26922-26944. doi: 10.3934/math.20231378

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Abstract

Our aim of this work is to approximate the fixed points of generalized $ \alpha _{m} $-nonexpansive mappings employing $ AA $-iterative scheme in the structure of modular spaces. The results of fixed points for generalized $ \alpha _{m} $-nonexpansive mappings is proven in this context. Moreover, the stability of the scheme and data dependence results are given for $ m $-contraction mappings. In order to demonstrate that the $ AA $-iterative scheme converges faster than some other schemes for generalized $ \alpha_{m} $-nonexpansive mappings, numerical examples are shown at the end.

References

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