A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition

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.