The authors study the generalized variational inequality problem of finding such that
where is a nonempty closed convex subset of a smooth Banach space , is an accretive operator of into , is the duality mapping of into , and is the duality paring between and . To solve this problem, the authors propose the following iterative scheme: and
for , where is a sunny nonexpansive retraction from onto , is a sequence in , and is a sequence of real numbers.
For this iterative scheme, the authors establish a weak convergence result (Theorem 3.1) in a uniformly convex and 2-uniformly smooth Banach space for an -inverse strongly accretive operator. Applications to finding a zero point of an inverse strongly accretive operator and to finding a fixed point of a strictly pseudocontractive mapping are given.