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The Mann-type extragradient iterative algorithms with regularization for solving variational inequality problems, split feasibility, and fixed point problems. (English) Zbl 1383.47010

Summary: The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set \(\Xi\) of a general system of variational inequalities, the solution set \(\Gamma\) of a split feasibility problem, and the fixed point set \(\text{Fix}(S)\) of a strictly pseudocontractive mapping \(S\) in the setting of Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration 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)]. Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of \(\text{Fix}(S) \cap \Xi \cap \Gamma\) under mild conditions.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems

Citations:

Zbl 1130.90055
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Full Text: DOI

References:

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