Multiple-sets Split Feasibility Research Articles

A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Hybrid iterative methods for multiple sets split feasibility problems

Hybrid iterative methods for multiple sets split feasibility problems

A shrinking projection method for solving the split common null point problem in Banach spaces

In this paper, in order to solve the split common null point problem, we investigate a new explicit iteration method, base on the shrinking projection method and e-enlargement of a maximal monotone operator. We also give some applications of our main results for the problem of split minimum point, multiple-sets split feasibility, and split variational inequality. Two numerical examples also are given to illustrate the effectiveness of the proposed algorithm.

A cyclic iterative method for solving Multiple Sets Split Feasibility Problems in Banach Spaces

In this paper, we construct an iterative scheme and prove strong convergence theorem of the sequence generated to an approximate solution to a multiple sets split feasibility problem in a p-uniformly convex and uniformly smooth real Banach space. Some numerical experiments are given to study the efficiency and implementation of our iteration method. Our result complements the results of F. Wang (A new algorithm for solving the multiple-sets split feasibility problem in Banach spaces, Numerical Functional Anal. Optim. 35 (2014), 99–110), F. Scho¨pfer et al. (An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems 24 (2008), 055008) and many important recent results in this direction.

Algorithms for nonexpansive self-mappings with application to the constrained multiple-set split convex feasibility fixed point problem in Hilbert spaces

In this article we devise two iteration schemes for approximating common fixed points of a finite family of nonexpansive mappings and establish the corresponding strong convergence theorem for the sequence generated by any one of our algorithms. Then we apply our results to approximate a solution of the so-called constrained multiple-set convex feasibility fixed point problem for firmly nonexpansive mappings which covers the multiple-set convex feasibility problem in the literature. In particular, our algorithms can be used to approximate the zero point problem of maximal monotone operators, and the equilibrium problem. Furthermore, the unique minimum norm solution can be obtained through our algorithms for each mentioned problem.

Strong Convergence Theorem for Multiple Sets Split Feasibility Problems in Banach Spaces

ABSTRACTThe purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems in p-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions in p-uniformly convex real Banach spaces that are also uniformly smooth.

Strong convergence theorems for generalized nonexpansive mappings on star-shaped set with applications

In this paper, we study attractive points for a class of generalized nonexpansive mappings on star-shaped sets and establish strong convergence theorems of the Halpern iterative sequences generated by these mappings in a real Hilbert space. We modify Halpern’s iterations for finding an attractive point of a mapping T satisfying condition (E) on a star-shaped set C in a real Hilbert space H and provide an affirmative answer to an open problem posed by Akashi and Takahashi in a recent work of (Appl. Math. Comput. 219(4):2035-2040, 2012) for nonexpansive and nonspreading mappings. Furthermore, we study the approximation of common attractive points of generalized nonexpansive mappings and derive a strong convergence theorem by a new iteration scheme for these mappings. As applications of our results, we study multiple sets split monotone inclusion problems for inverse strongly monotone mappings, multiple sets split optimization problems, and multiple sets split feasibility problems. Our results contain many original results on multiple sets split feasibility problem in the literature. Our results also improve and generalize many well-known results in the current literature. MSC:47H10, 37C25.

Solutions for a variational inclusion problem with applications to multiple sets split feasibility problems

In this paper, we first study the set of common solutions for two variational inclusion problems in a real Hilbert space and establish a strong convergence theorem of this problem. As applications, we study unique minimum norm solutions of the following problems: multiple sets split feasibility problems, system of convex constrained linear inverse problems, convex constrained linear inverse problems, split feasibility problems, convex feasibility problems. We establish iteration processes of these problems and show the strong convergence theorems of these iteration processes.MSC:47J20, 47J25, 47H05, 47H09.

Hierarchical problems with applications to mathematical programming with multiple sets split feasibility constraints

In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints.