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 -
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 aunique 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 $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming 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 -