  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.
