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In this paper, we propose and study several strongly convergent versions ofthe forward-reflected-backward splitting method of Malitsky and Tam for findinga zero of the sum of two monotone operators in a real Hilbert space. Ourproposed methods only require one forward evaluation of the single-valuedoperator and one backward evaluation of the set-valued operator at eachiteration; a feature that is absent in many other available strongly convergentsplitting methods in the literature. We also develop inertial versions of ourmethods and strong convergence results are obtained for these methods when theset-valued operator is maximal monotone and the single-valued operator isLipschitz continuous and monotone. Finally, we discuss some examples from imagerestorations and optimal control regarding the implementations of our methodsin comparison with known related methods in the literature.

Strong Convergence of Forward-Reflected-Backward Splitting Methods for  Solving Monotone Inclusions with Applications to Image Restoration and  Optimal Control