Construction algorithms for a class of monotone variational inequalities

This paper is devoted to solve the following monotone variational inequality of finding x ∗ ∈ Fix ( T ) such that ⟨ A x ∗ , x - x ∗ ⟩ ≥ 0 , ∀ x ∈ Fix ( T ) , where 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.