On solving proximal split feasibility problems and applications

Witthayarat, Uamporn; Cho, Yeol Je; Cholamjiak, Prasit

doi:10.1215/20088752-2017-0028

Cited by 9 publications

(3 citation statements)

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“…It has been found that the SFP can also be used in the air traffic flow management problems. Many researchers studied the SFP and introduced various algorithms to solve it (see [5][6][7][8][9][10][11][12][13][14][15] and references therein). The original algorithm introduced in [1] involves the computation of the inverse A −1 (assuming the existence of the inverse of A) and thus does not become popular.…”

Section: Introductionmentioning

confidence: 99%

Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

2019

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The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

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Section: Introductionmentioning

confidence: 99%

Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

2019

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“…In what follows, we use Γ to denote the solution set of the problem (2). The above problem (2) has been studied extensively in the literature, see for instance [31][32][33][34][35]. In order to solve problem (2), in [36], Moudafi and Thakur presented the following split proximal algorithm.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Approach to the Solutions of Proximal Split Feasibility Problems

Zhu

Yao

2019

Mathematics

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“…It is remarked that some related best proximity point theorems for proximal contractions, proximal cyclic contractions and cyclic contractions can be found in the references [4][5][6][7][10][11][12]. Further, some applications of proximality can be found in the references [2,9].…”

Section: Introductionmentioning

confidence: 99%

Best proximity point theorems for supreme proximal contractions

Basha

2019

Ann. Funct. Anal.

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This article presents some best proximity point theorems for new classes of nonself mappings, called supreme proximal contractions and supreme proximal cyclic contractions, which are brought forth to generalize the notion of self-contraction. Eventually, these results explore the existence of best proximity points that serve as optimal approximate solutions to the fixed point equations of the form T x = x, where T is a supreme proximal contraction or a supreme proximal cyclic contraction. Further, it is interesting to observe that such results generalize the most celebrated and elegant Banach's contraction to the case of non-self mappings.

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On solving proximal split feasibility problems and applications

Cited by 9 publications

References 0 publications

Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

An Iterative Approach to the Solutions of Proximal Split Feasibility Problems

Best proximity point theorems for supreme proximal contractions

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