scholarly journals On the Shrinking Projection Method for the Split Feasibility Problem in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Huanhuan Cui ◽  
Haixia Zhang
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Shrinking Projection Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, we consider the split feasibility problem in Banach spaces. By applying the shrinking projection method, we propose an iterative method for solving this problem. It is shown that the algorithm under two different choices of the stepsizes is strongly convergent to a solution of the problem.

A new iterative method for the split feasibility problem

2018 ◽  
Vol 34 (3) ◽  
pp. 313-320
Author(s):  
QIAO-LI DONG ◽  
◽  
DAN JIANG ◽  
Keyword(s):  
Inverse Problems ◽  
Linear Operator ◽  
Iterative Method ◽  
Projection Method ◽  
Numerical Experiments ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
New Iterative Method

The split feasibility problem (SFP) has many applications, which can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. In this paper, we introduce a new projection method to solve the SFP and prove its convergence under standard assumptions. Our results improve previously known corresponding methods and results of this area. The preliminary numerical experiments illustrates the advantage of our proposed methods.

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.

scholarly journals An Explicit Method for the Split Feasibility Problem with Self-Adaptive Step Sizes

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Youli Yu
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Explicit Method ◽  
The Split Feasibility Problem ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

An explicit iterative method with self-adaptive step-sizes for solving the split feasibility problem is presented. Strong convergence theorem is provided.

scholarly journals The Split Feasibility Problem with Some Projection Methods in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Toshiharu Kawasaki ◽  
Hiroko Manaka
Keyword(s):  
Banach Spaces ◽  
Metric Projection ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Equivalent Equation ◽  
The Split Feasibility Problem ◽  
Sunny Generalized Nonexpansive Retraction ◽  
Split Feasibility ◽  
Mathematical Programing

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

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