Comments on relaxed $(\gamma, r)$-cocoercive mappings


Department of Mathematics, University of Kurdistan, Sanandaj 416, Kurdistan, Iran.


We show that the variational inequality $VI(C,A)$ has a
unique solution for a relaxed $(gamma , r)$-cocoercive,
$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where
$C$ is a nonempty closed convex subset of a Hilbert space $H$. From
this result, it can be derived that, for example, the recent
algorithms given in the references of this paper, despite their
becoming more complicated, are not general as they should be.