A theorem of variational inclusion problems and various nonlinear mappings

Khuangsatung, Wongvisarut; Kangtunyakarn, Atid

doi:10.1080/00036811.2017.1307965

Cited by 4 publications

(12 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…n for all n ∈ N. 4). We compare our proposed algorithm (Algorithm 1) with the algorithm in [28]. The control parameters are set as follows: ξ = 0.5, ρ = 0.015, ω = 1.5, δ 1 = 0.5, δ 2 = 0.5, and µ = 0.5.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In 2014, Khuangsatung and Kangtunyakarn [27,28] presented the modified variational inclusion problem (MVIP), that is, to find u ∈ H such that the following holds:…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the ideas of [26,28,31], we provide a new method for determining the solution set of the modified variational inclusion problem in Hilbert spaces. For obtaining high performance, our method modifies the relaxed inertial Tseng's type method by using the condition ∑ n i=1 δ i = 1 and the parallel technique, which finds the farthest element Ā.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications

et al. 2021

View full text Add to dashboard Cite

The goal of this study was to show how a modified variational inclusion problem can be solved based on Tseng’s method. In this study, we propose a modified Tseng’s method and increase the reliability of the proposed method. This method is to modify the relaxed inertial Tseng’s method by using certain conditions and the parallel technique. We also prove a weak convergence theorem under appropriate assumptions and some symmetry properties and then provide numerical experiments to demonstrate the convergence behavior of the proposed method. Moreover, the proposed method is used for image restoration technology, which takes a corrupt/noisy image and estimates the clean, original image. Finally, we show the signal-to-noise ratio (SNR) to guarantee image quality.

show abstract

Section: Numerical Experimentsmentioning

confidence: 99%

“…In 2014, Khuangsatung and Kangtunyakarn [27,28] presented the modified variational inclusion problem (MVIP), that is, to find u ∈ H such that the following holds:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications

et al. 2021

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…We know that variational inclusion problems includes optimization problems, variational inequalities problems, and equilibrium problems as special cases. The classical methods for solving this problem are plenty of different ways by many authors (see other works [13][14][15][16] for examples). However, a popular method for solving the problem (5) is the forward-backward splitting method in a Hilbert space H which was first introduced by Combettes and Hirstoaga 17 in 2005.…”

mentioning

confidence: 99%

A new algorithm for split variational inclusion and fixed point problems in Banach spaces

Puangpee

Suantai

2020

Comp and Math Methods

View full text Add to dashboard Cite

In this article, we introduce a new algorithm for finding a solution element of the split variational inclusion problem which is also a fixed point of a nonexpansive mapping in a uniformly convex and smooth Banach space. A strong convergence theorem of the proposed algorithm is established under some suitable control conditions. Our main result can reduce to study several variational inclusion problems, null point problems, and fixed point problems in both Hilbert and Banach spaces. Numerical experiments to illustrate the convergence behavior of our proposed algorithm are given. Moreover, we also apply our results to solve the image restoration problems.

show abstract

An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application

et al. 2023

View full text Add to dashboard Cite

In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for increased acceleration. Moreover, we demonstrate that the proposed method strongly converges under appropriate conditions and apply the proposed method to solve the image restoration problem where the images have been subjected to various obscuring processes. In our example, we use the proposed method and Khuangsatung and Kangtunyakarn’s method to restore two medical images. To compare image quality, we also evaluate the signal-to-noise ratio (SNR) of the proposed method to that of Khuangsatung and Kangtunyakarn’s method.

show abstract

A theorem of variational inclusion problems and various nonlinear mappings

Cited by 4 publications

References 29 publications

A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications

A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications

A new algorithm for split variational inclusion and fixed point problems in Banach spaces

An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application

Contact Info

Product

Resources

About