The Method for Solving Fixed Point Problem of G-Nonexpansive Mapping in Hilbert Spaces Endowed with Graphs and Numerical Example

Khuangsatung, Wongvisarut; Kangtunyakarn, Atid

doi:10.1007/s13226-020-0391-y

Cited by 2 publications

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References 17 publications

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“…1,7) and t = (0.22, 1, 7), this implies that Θ 1 s − Θ 1 t > 0.1 > s − t . Θ 2 is not nonexpansive since for s = (5, −0.5, 2.11) and t = (5, −0.5, 2.28), we have Θ 2 s − Θ 2 t > 0.3 > s − t .…”

mentioning

confidence: 92%

“…Many problems in mathematical sciences have been solved by finding a fixed-point approximation of a nonexpansive mapping in many metric spaces. Iterative sequences have been proposed for finding fixed points and their applications by many mathematicians, see [1][2][3]. One of the most famous is the S-iteration method introduced by Agarwal et al [4] for some operators in norm linear spaces.…”

Section: Introductionmentioning

confidence: 99%

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Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery

et al. 2022

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This article considers a parallel monotone hybrid algorithm for a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes for finding a common fixed point by the two different hybrid projection methods. Moreover, we show the computational performance of our algorithm in comparison to some methods. Strong convergence theorems are proved under suitable conditions. Finally, we give some numerical experiments of our algorithms to show the efficiency and implementation of the LASSO problems in signal recovery with different types of blurred matrices and noise.

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confidence: 92%

Section: Introductionmentioning

confidence: 99%

Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery

et al. 2022

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Approximation of G-variational inequality problems and fixed-point problems of G-κ-strictly pseudocontractive mappings by an intermixed method endowed with a graph

Sripattanet

Kangtunyakarn

2023

J Inequal Appl

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In this paper, we first study G-κ-strictly pseudocontractive mappings and we establish a strong convergence theorem for finding the fixed points of two G-κ-strictly pseudocontractive mappings, two G-nonexpansive mappings, and two G-variational inequality problems in a Hilbert space endowed with a directed graph without the Property G. Moreover, we prove an interesting result involving the set of fixed points of a G-κ-strictly pseudocontractive and G-variational inequality problem and if Λ is a G-κ-strictly pseudocontractive mapping, then $I-\Lambda $ I − Λ is a $G-\frac{(1-\kappa )}{2}$ G − ( 1 − κ ) 2 -inverse strongly monotone mapping, shown in Lemma 3.3. In support of our main result, some examples are also presented.

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The Method for Solving Fixed Point Problem of G-Nonexpansive Mapping in Hilbert Spaces Endowed with Graphs and Numerical Example

Cited by 2 publications

References 17 publications

Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery

Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery

Approximation of G-variational inequality problems and fixed-point problems of G-κ-strictly pseudocontractive mappings by an intermixed method endowed with a graph

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