This paper is devoted to solve the following monotone variational inequality of finding x * ∈ Fix(T ) such thatwhere A is a monotone operator and Fix(T ) is the set of fixed points of nonexpansive operator T . For this purpose, we construct an implicit algorithm and prove its convergence hierarchical to the solution of above monotone variational inequality.
The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we give some strong convergence theorems for the proximal split feasibility problems.MSC: 49J53; 65K10; 49M37; 90C25
The proximal split feasibility problem has been studied. A regularized method has been presented for solving the proximal split feasibility problem. Strong convergence theorem is given.
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