宇宙发散、弱宇宙收敛与无穷远处的不动点
Cosmic Divergence, Weak Cosmic Convergence, and Fixed Points at Infinity
摘要：
为了刻画无不动点的非扩张算子的不动点迭代的渐近行为，Bauschke等人[不动点理论应用（2016）]最近研究了宇宙收敛，并证明宇宙收敛总是成立。本文给出了一个大规模发散的反例，证明了这个猜想是错误的。本文还通过一个反例证明了宇宙收敛在无限维中是弱的。最后，本文展示了与宇宙收敛有关的积极结果，这些结果提供了一种解释，即宇宙聚集点是无穷远处的不动点。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
