Abstract. New algorithms are proposed to solve a system of operator inclusions with monotone operators acting in a Hilbert space. The algorithms are based on three well-known methods: the Tseng forward-backward splitting algorithm and two hybrid algorithms for approximation of fixed points of nonexpansive operators. Theorems on the strong convergence of the sequences generated by the algorithms are proved. Refs: 40 titles.

Keywords: operator inclusion, maximum monotone operator, resolvent, Hilbert space, Tseng splitting algorithm, hybrid algorithm, strong convergence.