  We develop a fixed-point extension of quantitative equational logic and give
semantics in one-bounded complete quantitative algebras. Unlike previous
related work about fixed-points in metric spaces, we are working with the
notion of approximate equality rather than exact equality. The result is a
novel theory of fixed points which can not only provide solutions to the
traditional fixed-point equations but we can also define the rate of
convergence to the fixed point. We show that such a theory is the quantitative
analogue of a Conway theory and also of an iteration theory; and it reflects
the metric coinduction principle. We study the Bellman equation for a Markov
decision process as an illustrative example.
