Fixed point operators are heavily used in abstract interpretation (https://secure.wikimedia.org/wikipedia/en/wiki/Abstract_inte...), which in turn is used in static analysis of programs for automatic bug detection or compiler optimizations. In certain situations it can also be used to formally prove the correctness of a program. Just to give a concrete example, this is a static analyzer based on abstract interpretation: http://www.astree.ens.fr/ . Polyspace (https://secure.wikimedia.org/wikipedia/en/wiki/Polyspace) is another static analysis tool that uses abstract interpretation.