  In this paper, we study the nonexpansive properties of a generalized
forward-backward splitting (G-FBS) operator, particularly under the setting of
degenerate metric, from which follow the convergence results in terms of
degenerate metric of the associated fixed-point iterations. The descent lemma
and sufficient decrease property are also extended to degenerate case. It is
further shown that the G-FBS operator provides a simplifying and unifying
framework to model and analyze a great variety of operator splitting
algorithms, many existing results are exactly recovered or relaxed from our
general results.
