Map Transformation to Force Convergence to Unique Fixed Point

I posted a question on MathOverflow at http://mathoverflow.net/questions/49202/map-transformation-to-force-convergence-to-unique-fixed-point. The question has to do with forcing convergence to a fixed point which is known to exist and be unique. The posted question refers to this document which contains and elaborates on the question: http://math.gillesgnacadja.info/files/FixedPointAlgo_OPEN.html.

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