scholarly journals A Viscosity Approximation Method for the Split Feasibility Problems in Hilbert Space

2017 ◽  
Vol 9 (1) ◽  
pp. 84
Author(s):  
Li Yang
Keyword(s):  
Hilbert Space ◽  
Approximation Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, the most basic idea is to apply the viscosity approximation method to study the split feasibility problem (SFP), we will be in the infinite-dimensional Hilbert space to study the problem . We defined $x_{0}\in C$ as arbitrary and $x_{n+1}=(1-\alpha_{n})P_{C}(I-\lambda_{n}A^{*}(I-P_{Q})A)x_{n}+\alpha_{n}f(x_{n})$, for $n\geq0,$ where $\{\alpha_{n}\}\subset(0,1)$. Under the proper control conditions of some parameters, we show that the sequence $\{x_{n}\}$  converges strongly to a solution of SFP. The results in this paper extend and further improve the relevant conclusions in Deepho (Deepho, J. \& Kumam, P., 2015).

scholarly journals A Modified Halpern's Iterative Scheme for Solving Split Feasibility Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Jitsupa Deepho ◽  
Poom Kumam
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The purpose of this paper is to introduce and study a modified Halpern’s iterative scheme for solving the split feasibility problem (SFP) in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu (Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018) and some others.

scholarly journals A Strongly Convergent Method for the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Naseer Shahzad
Keyword(s):  
Hilbert Spaces ◽  
Extragradient Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Convergence Point ◽  
Convergent Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
Regularized Method

The purpose of this paper is to introduce and analyze a strongly convergent method which combined regularized method, with extragradient method for solving the split feasibility problem in the setting of infinite-dimensional Hilbert spaces. Note that the strong convergence point is the minimum norm solution of the split feasibility problem.

scholarly journals An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Hammed Anuoluwapo Abass ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

scholarly journals Strong Convergence on the Split Feasibility Problem by Mixing W -Mapping

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fugen Gao ◽  
Xiaoxiao Liu ◽  
Xiaochun Li
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, we concern with the split feasibility problem (SFP) in real Hilbert space whenever the sets involved are nonempty, closed, and convex. By mixing W -mapping with the viscosity, we introduce a new iterative algorithm for solving the split feasibility problem, and we prove that our proposed algorithm is convergent strongly to a solution of the split feasibility problem.

scholarly journals A New Extragradient-Type Algorithm for the Split Feasibility Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Yazheng Dang ◽  
Yan Gao ◽  
Bo Wang
Keyword(s):  
Hilbert Spaces ◽  
Extragradient Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Subgradient Extragradient Method ◽  
Type Method ◽  
Infinite Dimensional ◽  
Type Algorithm ◽  
The Split Feasibility Problem ◽  
Split Feasibility

We consider the split feasibility problem (SFP) in Hilbert spaces, inspired by extragradient method presented by Ceng, Ansari for split feasibility problem, subgradient extragradient method proposed by Censor, and variant extragradient-type method presented by Yao for variational inequalities; we suggest an extragradient-type algorithm for the SFP. We prove the strong convergence under some suitable conditions in infinite-dimensional Hilbert spaces.

An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

2021 ◽  
pp. 2250120
Author(s):  
Yan Tang ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Banach Spaces ◽  
Split Feasibility Problem ◽  
Null Point ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Inertial Algorithm ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.

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