Document Type : Research Paper

Author

• S. Saeidi

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

Abstract

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.

Keywords

• Common element
• Contraction
• Fixed point
• Iteration
• Nonexpansive mapping
• Relaxed $(gamma , r)$-cocoercive mappings
• variational inequality