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

In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method Malitsky Tam for finding a zero sum two monotone operators in real Hilbert space. Our proposed methods only require one forward evaluation single-valued operator backward set-valued at each iteration; feature that is absent many other available literature. We also develop inertial our strong convergence results are obtained these when maximal Lipschitz continuous monotone. Finally, discuss some examples from image restorations optimal control regarding implementations comparisons with known related