IMPLICIT VISCOSITY ITERATIVE ALGORITHM FOR THE SPLIT EQUILIBRIUM PROBLEM AND THE FIXED POINT PROBLEM FOR ONE-PARAMETER NONEXPANSIVE SEMIGROUPS (Nonlinear Analysis and Convex Analysis)
In this paper, we introduce and study a new viscosity approximation method by modify the hybrid s... more In this paper, we introduce and study a new viscosity approximation method by modify the hybrid steepest descent method for finding a common solution of split variational inclusion problem and fixed point problem of a countable family of nonexpansive mappings. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and fixed point problem for a countable family of nonexpansive mappings which is the unique solution of the variational inequality problem. The results present in this paper are the supplement, extension and generalization of the previously known results in this area. Numerical results demonstrate the performance and convergence of our result that the algorithm converges to a solution to a concrete split variational inclusion problem and fixed point problem.
We introduced an implicit and an explicit iteration method based on the hybrid steepest descent m... more 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.
The purpose of this paper is to introduce and analyze a weakly convergent theorem by using the re... more 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 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) ∩ under mild assumptions. MSC: 47H09; 47J25; 65K10
The purpose of this paper is to introduce and analyze Mann's type extragradient for finding a com... more The purpose of this paper is to introduce and analyze Mann's type extragradient for finding a common solution set 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) ∩ 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 and some others. MSC: 49J40; 47H05
The purpose of this paper is to introduce and study a modified Halpern's iterative scheme for sol... more 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.
Uploads
Papers by Jitsupa Deepho