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Received September 5, 2021; Accepted November 20, 2021; Published December 19, 2021
Abstract. In this paper, we propose a new iterative algorithm, which is based on the linear search method to solve a split variational inclusion problem in two Hilbert spaces. Our iteration algorithm does not involve projection operators, and the step-sizes do not depend on the operator norm. A weak convergence result on the solutions of the split variational inclusion problem is obtained. The split minimization problem and split feasibility problem are considered as two applications of our main results.
How to Cite this Article:
J.F. Xiong, Z.L. Ma, L.S. Zhang, Convergence theorems for the split variational inclusion problem in Hilbert spaces, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 40, pp. 1-12.