In this work, we consider a continuous dynamical system associated with the fixed point set of a nonexpansive operator which was originally studied by Boţ and Csetnek (J. Dyn. Diff. Equat. 29(1), pp. 155–168, 2017). Our main results establish convergence rates for the system’s trajectories when the nonexpansive operator satisfies an additional regularity property. This setting is the natural continuous-time analogue to discrete-time results obtained in Bauschke, Noll and Phan (J. Math. Anal. Appl. 421(1), pp. 1–20, 2015) and Borwein, Li and Tam (SIAM J. Optim. 27(1), pp. 1–33, 2017) by using the same regularity properties. Closure properties of the class of Hölder regular operators under taking convex combinations and compositions are also derived.

在这项工作中，我们考虑了一个与非膨胀算子的不动点集相关的连续动力系统，该系统最初由 Boţ 和 Csetnek 研究（J. Dyn. Diff. Equat. 29 (1), pp. 155–168, 2017） . 我们的主要结果确定了当非膨胀算子满足额外的规律性时系统轨迹的收敛率。此设置是对 Bauschke、Noll 和 Phan (J. Math. Anal. Appl. 421 (1), pp. 1–20, 2015) 和 Borwein, Li 和 Tam ( SIAM J. Optim. 27 (1), pp. 1–33, 2017) 使用相同的规律性属性。还导出了采用凸组合和组合的 Hölder 正则算子类的闭包性质。