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

Document Type : Research Paper


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.


Volume 1, Issue 1 - Serial Number 1
January 2010
Pages 54-57
  • Receive Date: 20 April 2009
  • Revise Date: 29 October 2009
  • Accept Date: 06 November 2009
  • First Publish Date: 01 January 2010