  Monotone inclusions have wide applications in solving various convex
optimization problems arising in signal and image processing, machine learning,
and medical image reconstruction. In this paper, we propose a new splitting
algorithm for finding a zero of the sum of a maximally monotone operator, a
monotone Lipschitzian operator, and a cocoercive operator, which is called
outer reflected forward-backward splitting algorithm. Under mild conditions on
the iterative parameters, we prove the convergence of the proposed algorithm.
As applications, we employ the proposed algorithm to solve composite monotone
inclusions involving monotone Lipschitzian operator, cocoercive operator, and
the parallel sum of operators. The advantage of the obtained algorithm is that
it is a completely splitting algorithm, in which the Lipschitzian operator and
the cocoercive operator are processed via explicit steps and the maximally
monotone operators are processed via their resolvents.
