  To characterize the asymptotic behavior of fixed-point iterations of
non-expansive operators with no fixed points, Bauschke et al. [Fixed Point
Theory Appl. (2016)] recently studied cosmic convergence and conjectured that
cosmic convergence always holds. This paper presents a cosmically divergent
counter example, which disproves this conjecture. This paper also demonstrates,
with a counter example, that cosmic convergence can be weak in infinite
dimensions. Finally, this paper shows positive results relating to cosmic
convergence that provide an interpretation of cosmic accumulation points as
fixed points at infinity.
