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Strong convergence of two inertial projection algorithms in Hilbert spaces

In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.