Ebrahim Soori - Department of Mathematics, Lorestan University, P.O. Box ۴۶۵, Khoramabad, Lorestan, Iran.

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi s Propositions for finding a unique solution of the variational inequality for $(u, v)$-cocoercive mappings in Banach spaces.

Variational inequality, Nonexpansive mapping, $(u, v)$-cocoercive mapping, Metric projection, Sunny nonexpansive retraction