TY - JOUR
ID - 68
TI - Comments on relaxed $(\gamma, r)$-cocoercive mappings
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Saeidi, S.
AD - Department of Mathematics, University of Kurdistan,
Sanandaj 416, Kurdistan, Iran.
Y1 - 2010
PY - 2010
VL - 1
IS - 1
SP - 54
EP - 57
KW - Common element
KW - Contraction
KW - Fixed point
KW - Iteration
KW - Nonexpansive mapping
KW - Relaxed $(gamma , r)$-cocoercive mappings
KW - variational inequality
DO - 10.22075/ijnaa.2010.68
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_68.html
L1 - https://ijnaa.semnan.ac.ir/article_68_35bfd7b5fbb5e640ce2b05e93c804d24.pdf
ER -