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Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces

Journal: Sahand Communications in Mathematical Analysis (Vol.13, No. 1)

Publication Date:

Authors : ;

Page : 83-92

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

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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.

Last modified: 2019-04-28 14:12:06