A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections

Satit Saejung; Satit Saejung

doi:10.3934/math.2023475

AIMS Mathematics

2023, Volume 8, Issue 4: 9436-9442. doi: 10.3934/math.2023475

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Research article

A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections

Satit Saejung ^,

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 08 January 2023 Revised: 04 February 2023 Accepted: 07 February 2023 Published: 16 February 2023
MSC : 47H09, 47H10

In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" ^[2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption.
- common fixed point,
- generalized $ \alpha $-nonexpansive mapping,
- weak convergence,
- strong convergence,
- uniformly convex Banach space,
- strictly convex Banach space
Citation: Satit Saejung. A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections[J]. AIMS Mathematics, 2023, 8(4): 9436-9442. doi: 10.3934/math.2023475

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Abstract

In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" ^[2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption.

References

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[2]	S. Rezapour, M. Iqbal, A. Batool, S. Etemad, T. Botmart, A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems, AIMS Mathematics, 8 (2023), 5980–5997. https://doi.org/10.3934/math.2023301 doi: 10.3934/math.2023301
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