Convergence analysis of modified Abbas iteration process for two G-nonexpansive mappings

Khatoon, Sabiya; Uddin, Izhar

doi:10.1007/s12215-020-00481-x

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…Recently, Thianwan and Yambangwai [7] introduced a new two-step iteration process involving two G-nonexpansive mappings and studied its convergence analysis in a uniformly convex Banach space endowed with a graph. There is vast literature in this direction for more details (see [8][9][10][11][12][13][14][15][16][17][18][19] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Khatoon

Uddin

Ali

et al. 2021

Journal of Function Spaces

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In this work, we study the convergence of a new faster iteration in which two G -nonexpansive mappings are involved in the setting of uniformly convex Banach spaces with a directed graph. Moreover, by constructing a numerical example, we show the fastness of our iteration procedure over other existing iteration procedures in the literature.

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Section: Introductionmentioning

confidence: 99%

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Khatoon

Uddin

Ali

et al. 2021

Journal of Function Spaces

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“…The approximating of a fixed point using an effective iterative technique is an important field of research. For instance, Khatoon and Uddin [27] studied Abbas' iterative scheme for G-nonexpansive operators while Wairojjana [28] proved strong convergence of a certain scheme for variational inequalities problems. Moreover, different authors made claims about the convergence speed of their iteration processes: according to the authors in [19], the Agarwal iteration converges faster than Mann's and has the same convergence speed as the Picard iteration.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

2021

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In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α,β)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.

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Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

Chairatsiripong

Yambangwai

Thianwan

2023

Demonstratio Mathematica

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In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

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Convergence analysis of modified Abbas iteration process for two G-nonexpansive mappings

Cited by 5 publications

References 22 publications

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

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Convergence analysis of modified Abbas iteration process for two G-nonexpansive mappings

Cited by 5 publications

References 22 publications

Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

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Product

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Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure