Strong convergence theorems for the split variational inclusion problem in Hilbert spaces. (English) Zbl 1476.47050
Summary: In this paper, we first consider a split variational inclusion problem and give several strong convergence theorems in Hilbert spaces, like the Halpern-Mann type iteration method and the regularized iteration method. As applications, we consider the algorithms for a split feasibility problem and a split optimization problem and give strong convergence theorems for these problems in Hilbert spaces. Our results for the split feasibility problem improve the related results in the literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47J22 | Variational and other types of inclusions |
Keywords:
zero point; split feasibility problem; resolvent mapping; optimization problem; split variational inclusion problem; strong convergence; Hilbert spaces; Halpern-Mann type iteration; regularized iterationReferences:
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