Jitsupa Deepho

A new Hybrid Projection Algorithm for Solving the Split Generalized Equilibrium Problems and the System of Variational Inequality Problems

In this paper, we introduced modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of the split generalized equilibrium problem and the set of solutions of the general system of the variational inequality problem for two-inverse strongly monotone mappings in real Hilbert spaces. The strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions are provided.

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

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.

Mann’s type extragradient for solving split feasibility and fixed point problems of Lipschitz asymptotically quasi-nonexpansive mappings

The purpose of this paper is to introduce and analyze Mann’s type extragradient for finding a common solution set Γ of the split feasibility problem and the set Fix(T) of fixed points of Lipschitz asymptotically quasi-nonexpansive mappings T in the setting of infinite-dimensional Hilbert spaces. Consequently, we prove that the sequence generated by the proposed algorithm converges weakly to an element of Fix(T)∩Γ under mild assumption. The result presented in the paper also improves and extends some result of Xu (Inverse Probl. 26:105018, 2010; Inverse Probl. 22:2021-2034, 2006) and some others.MSC:49J40, 47H05.

Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings

The purpose of this paper is to introduce and analyze a weakly convergent theorem by using the regularized method and the relaxed extragradient method for finding a common element of the solution set Γ of the split feasibility problem and Fix(T) of fixed points of asymptotically quasi-nonexpansive mappings T in the setting of infinite-dimensional Hilbert spaces. Consequently, we prove that the sequence generated by the proposed algorithm converges weakly to an element of Fix(T)∩Γ under mild assumptions.MSC:47H09, 47J25, 65K10.

Modified Hybrid Steepest Method for the Split Feasibility Problem in Image Recovery of Inverse Problems

ABSTRACT In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; where {αn}⊂(0,1). It is noted that Xu’s original iterative method can conclude only weak convergence. Consequently, we obtain the sequence {xn} generated by our iteration method converges strongly to , where is the unique solution of the variational inequality Our result extends and improves the result of Xu, as shown in the literature, from weak to strong convergence theorems. Finally, in the last section, numerical examples for study behavior convergence analysis of this algorithm are obtained.

An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems

ABSTRACT In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section.

Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of split variational inclusion problem in the framework Hilbert spaces. Strong convergence theorem of the sequences generated by the purpose iterative scheme is obtained. In the last section, we present some computational examples to illustrate the assumptions of the proposed algorithms.

A Viscosity Approximation Method for the Split Feasibility Problems

In this paper, we discuss the strong convergence of the viscosity approximation method for solving the split feasibility problem in Hilbert spaces. Consider also the iteration process \( \{ x_{n} \} \), where \( x_{0} \in C \) is arbitrary and \( x_{n + 1} = (1 - \alpha_{n} )P_{C} (I - \xi A^{*} (I - P_{Q} )A)x_{n} + \alpha_{n} f(x_{n} ),n \ge 1 \) where \( \alpha_{n} \in (0,1) \). The main result present in this paper improve and extend some recent result done by Xu [Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018] and some others.

The Hybrid Steepest Descent Method for Split Variational Inclusion and Constrained Convex Minimization Problems

We introduced an implicit and an explicit iteration method based on the hybrid steepest descent method for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem.