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.
Inspired by the very recent results of Wang and Xu (2010), we study properties of the approximating curve with 1-norm regularization method for the split feasibility problem (SFP). The concept of the minimum-norm solution set of SFP in the sense of 1-norm is proposed, and the relationship between the approximating curve and the minimum-norm solution set is obtained.
We study the split feasibility problem (SFP) involving the fixed point
problems (FPP) in the framework of p-uniformly convex and uniformly smooth
Banach spaces. We propose a Halpern-type iterative scheme for solving the
solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then
we prove its strong convergence theorem of the sequences generated by our
iterative scheme under implemented conditions. We finally provide some
numerical examples and demonstrate the efficiency of the proposed algorithm.
The obtained result of this paper complements many recent results in this
direction.
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.
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.
A Note on Approximating Curve with 1-Norm Regularization Method for the Split Feasibility Problem