Strong convergence theorems for the split variational inclusion problem in Hilbert spaces

By Chih-Sheng Chuang. Fixed Point Theory and Applications, 2013

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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:47H10, 49J40, 54H25.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

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