A modification of the forward-backward splitting method for monotone inclusions

In this work, we propose a new splitting method for monotone inclusion problems with three operators in real Hilbert spaces, in which one is maximal monotone, one is monotone-Lipschitz and one is cocoercive. By specializing in two operator inclusion, we recover the forward-backward and the generalization of the reflected-forward-backward splitting methods as particular cases. The weak convergence of the algorithm under standard assumptions is established. The linear convergence rate of the proposed method is obtained under an additional condition like the strong monotonicity. We also give some theoretical comparisons to demonstrate the efficiency of the proposed method.