Abstract. In this paper, new algorithms are proposed to solve operator inclusion problems with maximal monotone operators acting in a Hilbert space. The algorithms are based on inertial extrapolation and three well-known methods: 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.

Keywords: operator inclusion problem, maximal monotone operator, Hilbert space, inertial method, Tseng algorithm, hybrid algorithm, strong convergence.

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

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