TY - JOUR
T1 - Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces
AU - Hieu, Pham Thanh
AU - Thuy, Nguyen Thi Thu
AU - Strodiot, Jean Jacques
PY - 2019/3/15
Y1 - 2019/3/15
N2 - The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.
AB - The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.
KW - Accretive mapping
KW - Common fixed point
KW - Explicit method
KW - Nonexpansive semigroup
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85064004293&partnerID=8YFLogxK
U2 - 10.1007/s40840-017-0494-8
DO - 10.1007/s40840-017-0494-8
M3 - Article
AN - SCOPUS:85064004293
VL - 42
SP - 467
EP - 483
JO - Bulletin of the Malaysian Mathematical Sciences Society
JF - Bulletin of the Malaysian Mathematical Sciences Society
SN - 0126-6705
IS - 2
ER -