Revisiting jointly firmly nonexpansive families of mappings
Andrei Sipoş · Optimization · 2021
Recently, the author, together with L. Leuştean and A. Nicolae, introduced the notion of jointly firmly nonexpansive families of mappings in order to investigate in an abstract manner the convergence of proximal methods. Here, we further the study of this concept, by giving a characterization in terms of the classical resolvent identity, by improving on the rate of convergence previously obtained for the uniform case, and by giving a treatment of the asymptotic behaviour at infinity of such families.