TY - JOUR
ID - 25887
TI - Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Soori, Ebrahim
AD - Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran.
Y1 - 2019
PY - 2019
VL - 13
IS - 1
SP - 83
EP - 92
KW - Variational inequality
KW - Nonexpansive mapping
KW - $(u
KW - v)$-cocoercive mapping
KW - Metric projection
KW - Sunny nonexpansive retraction
DO - 10.22130/scma.2017.25887
N2 - Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let $u, v$ be positive numbers. In this paper, we show that the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for finding a unique solution of the variational inequality for $(u, v)$-cocoercive mappings in Banach spaces.
UR - http://scma.maragheh.ac.ir/article_25887.html
L1 - http://scma.maragheh.ac.ir/article_25887_4d361d95ff4721a03622269726d897e2.pdf
ER -