  In this paper a fixed-point solver for mappings from a Simplex into itself
that is gradient-free, global and requires $\binom{d+1}{ 2}$ function
evaluations for halvening the error is presented. It is based on topological
arguments and uses the constructive proof of the Mazurkewicz-Knaster-Kuratowski
lemma when used as part of the proof for Brouwers Fixed-Point theorem.
