Comments on relaxed $(γ, r)$-cocoercive mappings

Details Comments on relaxed $(γ, r)$-cocoercive mappings Comments on relaxed $(γ, r)$-cocoercive mappings

2009-09-23

arxiv.org/abs/0909.4291v1

Mathematics

Functional Analysis

Scientific paper

We show that the variational inequality $VI(C,A)$ has a unique solution for a relaxed $(\gamma, r)$-cocoercive, $\mu$-Lipschitzian mapping $A: C\to H$ 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.

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