Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 467-483 |
| Number of pages | 17 |
| Journal | Bulletin of the Malaysian Mathematical Sciences Society |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Mar 2019 |
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Keywords
- Accretive mapping
- Common fixed point
- Explicit method
- Nonexpansive semigroup
- Variational inequality
Cite this
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Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces. / Hieu, Pham Thanh; Thuy, Nguyen Thi Thu; Strodiot, Jean Jacques.
In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 42, No. 2, 15.03.2019, p. 467-483.Research output: Contribution to journal › Article
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 -