  The three-operators splitting algorithm is a popular operator splitting
method for finding the zeros of the sum of three maximally monotone operators,
with one of which is cocoercive operator. In this paper, we propose a class of
inertial three-operator splitting algorithm. The convergence of the proposed
algorithm is proved by applying the inertial Krasnoselskii-Mann iteration under
certain conditions on the iterative parameters in real Hilbert spaces. As
applications, we develop an inertial three-operator splitting algorithm to
solve the convex minimization problem of the sum of three convex functions,
where one of them is differentiable with Lipschitz continuous gradient.
Finally, we conduct numerical experiments on a constrained image inpainting
problem with nuclear norm regularization. Numerical results demonstrate the
advantage of the proposed inertial three-operator splitting algorithms.
