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In this paper, we introduce a general iterative method for a split variational inclusion and nonexpansive semigroups in Hilbert spaces. We also prove that the sequences generated by the proposed algorithm converge strongly to a common element of the set of solutions of a split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups, which also solves a class of variational inequalities as an optimality condition for a minimization problem. Moreover, a numerical example is given, to illustrate our methods and results, which may be viewed as a refinement and improvement of the previously known results announced by many other authors.

Iterative methods for split variational inclusion and fixed point problem of nonexpansive semigroup in Hilbert spaces