Abstract
In this paper, we first prove the strong convergence of viscosity approximation method for a modified Mann iteration process for asymptotically strict pseudocontractive mappings in intermediate sense, and then prove the strong convergence of general CQ algorithm for asymptotically strict pseudocontractive mappings in intermediate sense. We extend the concept of asymptotically strict pseudocontractive mappings in intermediate sense to Banach space setting, called nearly asymptotically k-strict pseudocontractive mapping in intermediate sense. We establish the weak convergence theorems for a fixed point of a nearly asymptotically K-strict pseudocontractive mapping in intermediate sense which is not necessarily Lipschitzian.
| Original language | English |
|---|---|
| Pages (from-to) | 283-308 |
| Number of pages | 26 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 11 |
| Issue number | 2 |
| State | Published - Aug 2010 |
| Externally published | Yes |
Keywords
- Asymptotically strict pseudocontractive mappings in intermediate sense
- Demiclosedness principle
- Fixed points
- Mann iteration process
- Strong and weak convergence theorems
- The CQ method
- Variational inequalities
- Viscosity approximation method
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics