In this paper, we first study the set of common solutions for two variational inclusion problems in a real Hilbert space and establish a strong convergence theorem of this problem. As applications, we study unique minimum norm solutions of the following problems: multiple sets split feasibility problems, system of convex constrained linear inverse problems, convex constrained linear inverse problems, split feasibility problems, convex feasibility problems. We establish iteration processes of these problems and show the strong convergence theorems of these iteration processes. MSC:47J20, 47J25, 47H05, 47H09.
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