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 |
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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 |
Keywords
- Accretive mapping
- Common fixed point
- Explicit method
- Nonexpansive semigroup
- Variational inequality