Summary: Let be a nonempty, closed convex subset of a Banach space . In this paper, motivated by Ya. I. Alber [Metric and generalized projection operators in Banach spaces: Properties and applications, in: A.G. Kartsatos (ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, in: Lect. Notes Pure Appl. Math. 178, Dekker, New York, 15–50 (1996; Zbl 0883.47083)], we introduce the following iterative scheme for finding a solution of the variational inequality problem for an inverse-strongly-monotone operator in a Banach space: and
for every , where is the generalized projection from onto , is the duality mapping from into and is a sequence of positive real numbers. Then we show a weak convergence theorem (Theorem 3.1). Finally, using this result, we consider the convex minimization problem, the complementarity problem, and the problem of finding a point satisfying .