Abstract
AbstractThe 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.
Highlights
Let H and H be two real Hilbert spaces and C ⊂ H and Q ⊂ H be two nonempty closed convex sets
The purpose of this paper is to study the following split feasibility and fixed point problems: Find x∗ ∈ C ∩ Fix(T) such that Ax∗ ∈ Q ∩ Fix(S)
In this paper, motivated by the work of Ceng et al [ ], Yao et al [ ], 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
Summary
Let H and H be two real Hilbert spaces and C ⊂ H and Q ⊂ H be two nonempty closed convex sets. In this paper, motivated by the work of Ceng et al [ ], Yao et al [ ], 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. We 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.
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