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An extragradient method for solving split feasibility and fixed point problems
- Source :
- Computers & Mathematics with Applications. 64:633-642
- Publication Year :
- 2012
- Publisher :
- Elsevier BV, 2012.
-
Abstract
- The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set @C of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191-201], we propose an iterative algorithm for finding an element of Fix(S)@[email protected] We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)@[email protected] under mild conditions.
- Subjects :
- Discrete mathematics
Weak convergence
Iterative method
Averaged mappings
Hilbert space
Solution set
Fixed point
Maximal monotone mappings
Regularization (mathematics)
Computational Mathematics
symbols.namesake
Monotone polygon
Computational Theory and Mathematics
Modelling and Simulation
Modeling and Simulation
Regularization
symbols
Split feasibility problems
Common element
Extragradient method
Fixed point problems
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 64
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....4800c4bb80dc9d7e31f9c3f04d485c64