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

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.

کلیدواژه ها:

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