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Chen, Jin-Zuo; Ceng, Lu-Chuan; Qiu, Yang-Qing; Kong, Zhao-Rong

Extra-gradient methods for solving split feasibility and fixed point problems. (English) Zbl 1346.47035

Fixed Point Theory Appl. 2015, Paper No. 192, 21 p. (2015).
Summary: The purpose of this paper is to study the extra-gradient methods for solving split feasibility and fixed point problems involved in pseudo-contractive mappings in real Hilbert spaces. We propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings with Lipschitz assumption. Moreover, we also suggest a Mann-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings without Lipschitz assumption. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility and fixed point problems. The results presented in this paper extend and improve some corresponding ones in the literature.

Cited in 1 Review
Cited in 12 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

Ishikawa-type iterative algorithm; Mann-type iterative algorithm; extra-gradient methods; split feasibility problems; fixed point problems; pseudo-contractive mappings
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References:

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