Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

Suparatulatorn, Raweerote; Khemphet, Anchalee; Charoensawan, Phakdi; Suantai, Suthep; Phudolsitthiphat, Narawadee

doi:10.1080/00207160.2019.1622687

Cited by 15 publications

(6 citation statements)

References 19 publications

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“…Both the demicontractive mapping and the strictly pseudocontractive mapping were studied by many authors. [1][2][3][4] Besides, Suparatulatorn et al 5 and Yao et al 6 considered the other case, which is the demicontractive mapping with coefficient ∈ [0, 1). Obviously, this case is contained in the demicontractive mapping with coefficient ∈ (− ∞, 1) that we are going to study.…”

Section: Introductionmentioning

confidence: 99%

An accelerated hybrid projection method with a self‐adaptive step‐size sequence for solving split common fixed point problems

Zhou

Tan

2021

Math Methods in App Sciences

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This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones. KEYWORDS demicontractive mapping, hybrid projection method, inertial technique, self-adaptive step-size sequence, split common fixed point problem MSC CLASSIFICATION 47H09; 47H10; 47J25; 65K15 INTRODUCTIONLet  be a Hilbert space with the norm || • || and the inner product ⟨• , •⟩ and F(K) be the fixed point set of a mapping K. Recall that the mapping K ∶  →  is said to be a strictly pseudocontractive if there exists a constant ∈ [0, 1) such thatBoth the demicontractive mapping and the strictly pseudocontractive mapping were studied by many authors. [1][2][3][4] Besides, Suparatulatorn et al. 5 and Yao et al. 6 considered the other case, which is the demicontractive mapping with coefficient ∈ [0, 1). Obviously, this case is contained in the demicontractive mapping with coefficient ∈ (− ∞, 1) that we are going to study. Meanwhile, the strictly pseudocontractive mapping with F(K) ≠ ∅ is the demicontractive mapping. The opposite is contradictory. Further, according to the properties of the norm and the inner product in Hilbert spaces, we know that the fixed point set of a demicontractive mapping is closed and convex.

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Section: Introductionmentioning

confidence: 99%

An accelerated hybrid projection method with a self‐adaptive step‐size sequence for solving split common fixed point problems

Zhou

Tan

2021

Math Methods in App Sciences

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“…For example, they are applicable to solve mechanics, traffic network problems, engineering, nonlinear programming, signal recovery, and image restoration. [1][2][3][4][5][6][7][8][9][10] To state the problems, we assume some notations that will be used for the rest of the paper as follows. Let H be a real Hilbert space and C a nonempty closed convex subset of H. Define F and  to be self-mapping operators on H. The variational inequality problem for F on C is a problem of finding x ∈ C satisfying the following inequality:…”

Section: Introductionmentioning

confidence: 99%

“…There have been a number of research works in variational inequality problems and fixed point problems, as some real‐world problems can be represented by these problems. For example, they are applicable to solve mechanics, traffic network problems, engineering, nonlinear programming, signal recovery, and image restoration 1–10 . To state the problems, we assume some notations that will be used for the rest of the paper as follows.…”

Section: Introductionmentioning

confidence: 99%

An inertial subgradient extragradient method of variational inequality problems involving quasi‐nonexpansive operators with applications

Suparatulatorn

Charoensawan

Khemphet

2021

Math Methods in App Sciences

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In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi-nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an application to a signal recovery in compressed sensing problem is shown as a numerical example of the algorithm. KEYWORDScompressed sensing, fixed point, inertial method, subgradient extragradient method, variational inequality MSC CLASSIFICATION 47J20; 90C25; 90C30; 90C52where Fix( ) represents the fixed point set of  .

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“…Many problems in various elds, such as image reconstruction [12,14,23] and signal processing [1,13,20,21,22,24], can be modeled as xed point problems. Numerous authors have presented various iterative approaches for xed point numerical approximation.…”

Section: Introductionmentioning

confidence: 99%

Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space

Chalarux

Chaichana

2021

Results in Nonlinear Analysis

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Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

Cited by 15 publications

References 19 publications

An accelerated hybrid projection method with a self‐adaptive step‐size sequence for solving split common fixed point problems

An accelerated hybrid projection method with a self‐adaptive step‐size sequence for solving split common fixed point problems

An inertial subgradient extragradient method of variational inequality problems involving quasi‐nonexpansive operators with applications

Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space

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