Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions of this principle which are compatible with the framework of more general families of mappings such as cocoercive and conically averaged mappings. As an application, we derive the weak convergence of the shadow sequence generated by the adaptive Douglas-Rachford algorithm.

中文翻译：

---

广义非扩展映射的半封闭性原则

半封闭原理是研究迭代方法收敛性的有力工具。例如，对于由 Douglas-Rachford 算法生成的阴影序列的弱收敛性，用于牢固非扩展映射的多算子半封闭性原则可用于获得简单透明的参数。我们提供了这一原则的扩展，这些扩展与更一般的映射系列的框架兼容，例如强制和圆锥平均映射。作为一个应用，我们推导出由自适应 Douglas-Rachford 算法生成的阴影序列的弱收敛性。