University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces83922588710.22130/scma.2017.25887ENEbrahimSooriDepartment of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran.Journal Article20160626Let $C$ 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.https://scma.maragheh.ac.ir/article_25887_4d361d95ff4721a03622269726d897e2.pdf