An accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings with applications to image recovery

Wattanataweekul, Rattanakorn; Janngam, Kobkoon

doi:10.1186/s13660-022-02796-y

Cited by 3 publications

(1 citation statement)

References 29 publications

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“…In the past decade, many researchers introduced algorithms for finding the fixed points of G-nonexpansive mappings; see [11][12][13][14]. Recently, Janngam et al [15][16][17] introduced fixed-point algorithms in Hilbert spaces with directed graphs and applied these results to classification and image recovery.…”

Section: Introductionmentioning

confidence: 99%

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Janngam

Suantai

2022

Mathematics

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In this paper, we propose a new accelerated common fixed-point algorithm for two countable families of G-nonexpansive mappings. Weak convergence results are obtained in the context of directed graphs in real Hilbert spaces. As applications, we apply the obtained results to solving some convex minimization problems and employ our proposed algorithm to solve the data classification of Breast Cancer, Heart Diseases and Ionosphere. Moreover, we also compare the performance of our proposed algorithm with other algorithms in the literature and it is shown that our algorithm has a better convergence behavior than the others.

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Section: Introductionmentioning

confidence: 99%

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Janngam

Suantai

2022

Mathematics

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On the complexity of a quadratic regularization algorithm for minimizing nonsmooth and nonconvex functions

Amaral,

Lopes,

Santos

et al. 2024

Optimization Methods and Software

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A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs

Khuangsatung,

Singta,

Kangtunyakarn

2024

J Inequal Appl

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This article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.

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An accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings with applications to image recovery

Cited by 3 publications

References 29 publications

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

On the complexity of a quadratic regularization algorithm for minimizing nonsmooth and nonconvex functions

A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs

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