ABSTRACT
Let K be a nonempty, closed and convex set in a real Hilbert space H, whose inner product and norm are denoted by ⋅ ⋅, and ⋅ , respectively. Let →T K H: be a nonlinear operator and S be a nonexpansive mapping. Let PK be the projection of H on K . Consider the problem of finding ∈u K , such that
− ≥ ∈Tu v u v K, 0, , (1.1)
which is known as the variational inequality introduced and studied by Stampacchia [1] in 1964.
