%0 Journal Article %T Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Soori, Ebrahim %D 2019 %\ 02/01/2019 %V 13 %N 1 %P 83-92 %! Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces %K Variational inequality %K Nonexpansive mapping %K $(u %K v)$-cocoercive mapping %K Metric projection %K Sunny nonexpansive retraction %R 10.22130/scma.2017.25887 %X 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. %U https://scma.maragheh.ac.ir/article_25887_4d361d95ff4721a03622269726d897e2.pdf