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We introduce and analyze an abstract algorithm that aims to find theprojection onto a closed convex subset of a Hilbert space. When specialized tothe fixed point set of a quasi nonexpansive mapping, the required sufficientcondition (termed "fixed-point closed") is less restrictive than the usualconditions based on the demiclosedness principle. A concrete example of asubgradient projector is presented which illustrates the applicability of thisgeneralization.

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