On the Nonexpansive Operators Based on Arbitrary Metric: A Degenerate Analysis

We in this paper study the nonexpansive operators equipped with arbitrary metric and investigate connections between firm nonexpansiveness, cocoerciveness averagedness. The convergence of associated fixed-point iterations is discussed particular focus on case degenerate metric, since degeneracy often encountered when reformulating many existing first-order operator splitting algorithms as a resolvent. This work paves way for analyzing generalized proximal point algorithm non-trivial relaxation step metric.