A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems

Shahram Rezapour; Maryam Iqbal; Afshan Batool; Sina Etemad; Thongchai Botmart; Shahram Rezapour; Maryam Iqbal; Afshan Batool; Sina Etemad; Thongchai Botmart

doi:10.3934/math.2023301

AIMS Mathematics

2023, Volume 8, Issue 3: 5980-5997. doi: 10.3934/math.2023301

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Research article

A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems

1.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
2.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4.
Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi, Pakistan
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 30 October 2022 Revised: 11 December 2022 Accepted: 19 December 2022 Published: 28 December 2022
MSC : 47H09, 47H10

This paper reports a modified F-iterative process for finding the fixed points of three generalized $ \alpha $-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized $ \alpha $-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized $ \alpha $-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized $ \alpha $-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.
- F-iteration,
- common fixed point,
- generalized $ \alpha $-nonexpansive mapping,
- convergence,
- condition (Ⅰ)
Citation: Shahram Rezapour, Maryam Iqbal, Afshan Batool, Sina Etemad, Thongchai Botmart. A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems[J]. AIMS Mathematics, 2023, 8(3): 5980-5997. doi: 10.3934/math.2023301

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Abstract

This paper reports a modified F-iterative process for finding the fixed points of three generalized $ \alpha $-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized $ \alpha $-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized $ \alpha $-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized $ \alpha $-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.

References

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