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An extragradient method for solving split feasibility and fixed point problems. (English) Zbl 1252.65102
Summary: The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set Γ 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 N. Nadezhkina and W. Takahashi [J. Optim. Theory Appl. 128, No. 1, 191–201 (2006; Zbl 1130.90055)], we propose an iterative algorithm for finding an element of Fix (S)Γ. We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix (S)Γ under mild conditions.

MSC:
65K10Optimization techniques (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
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