  The proximal extrapolated gradient method \cite{Malitsky18a} is an extension
of the projected reflected gradient method \cite{Malitsky15}. Both methods were
proposed for solving the classic variational inequalities. In this paper, we
investigate the projected reflected gradient method, in the general setting,
for solving monotone inclusions involving Lipschitzian operators. As a result,
we obtain a simple method for finding a zero point of the sum of two monotone
operators where one of them is Lipschizian. We also show that one can improve
the range of the stepsize of this method for the case when the Lipschitzian
operator is restricted to be cocoercive. A nice combination of this method and
the forward-backward splitting was proposed. As a result, we obtain a new
splitting method for finding a zero point of the sum of three operators (
maximally monotone + monotone Lipschitzian + cocoercive). Application to
composite monotone inclusions are demonstrated.
