A generalized forward–backward splitting operator: degenerate analysis and applications

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