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Hybrid Proximal-Type and Hybrid Shrinking Projection Algorithms for Equilibrium Problems, Maximal Monotone Operators, and Relatively Nonexpansive Mappings.
- Source :
- Numerical Functional Analysis & Optimization; Jul2010, Vol. 31 Issue 7, p763-797, 35p
- Publication Year :
- 2010
-
Abstract
- In this article, we introduce two hybrid proximal-type algorithms and two hybrid shrinking projection algorithms by using the hybrid proximal-type method and the hybrid shrinking projection method, respectively, for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of a relatively nonexpansive mapping, and the set of solutions to the equation 0 ∈ Tx for a maximal monotone operator T defined on a uniformly smooth and uniformly convex Banach space. The strong convergence of the sequences generated by the proposed algorithms is established. Our results improve and generalize several known results in the literature. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGORITHMS
EQUILIBRIUM
MATHEMATICAL sequences
STOCHASTIC convergence
BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 01630563
- Volume :
- 31
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Numerical Functional Analysis & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 52700054
- Full Text :
- https://doi.org/10.1080/01630563.2010.496697