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Strong convergence theorems for maximal monotone operators in Banach spaces.
- Source :
- Optimization; Aug2010, Vol. 59 Issue 6, p807-819, 13p
- Publication Year :
- 2010
-
Abstract
- Let E be a uniformly convex and uniformly smooth Banach space with the dual E* and let T : E → 2E* be a maximal monotone operator. By using the technique of resolvent operators and by using modified Ishikawa iteration and modified Halpern iteration for relatively non-expansive mappings, we suggest and analyse two iterative algorithms for finding an element x ∈ E such that 0 ∈ T(x). Strong convergence theorems for such iterative algorithms are proved. The ideas of these algorithms are applied to solve the problem of finding a minimizer of a convex function on E. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 59
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 52444514
- Full Text :
- https://doi.org/10.1080/02331930902839426