Abstract
In this paper, we consider a general system of nonlinear variational inequalities (in short, GSVI) in the setting of Banach spaces. We first establish the equivalence between GSVI and a system of fixed point problems. By utilizing this equivalence, we construct an implicit algorithm of Mann's type for solving GSNVI. We also propose another explicit algorithm of Mann's type for solving GSNVI. Finally, under very mild conditions, we prove the strong convergence of the sequences generated by the proposed algorithms.
| Original language | English |
|---|---|
| Pages (from-to) | 965-984 |
| Number of pages | 20 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 16 |
| Issue number | 5 |
| State | Published - 2015 |
Bibliographical note
Publisher Copyright:© 2015.
Keywords
- General system of nonlinear variational inequalities
- Inverse strongly accretive mappings
- Strictly pseudocontractive mappings
- Strongly accretive mappings
- Sunny non-expansive retraction
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics