  We introduce and analyze an abstract algorithm that aims to find the
projection onto a closed convex subset of a Hilbert space. When specialized to
the fixed point set of a quasi nonexpansive mapping, the required sufficient
condition (termed "fixed-point closed") is less restrictive than the usual
conditions based on the demiclosedness principle. A concrete example of a
subgradient projector is presented which illustrates the applicability of this
generalization.
