  We analyze inexact fixed point iterations where the generating function
contains an inexact solve of an equation system to answer the question of how
tolerances for the inner solves influence the iteration error of the outer
fixed point iteration. Important applications are the Picard iteration and
partitioned fluid structure interaction. We prove that the iteration converges
irrespective of how accurate the inner systems are solved, provided that a
specific relative termination criterion is employed, whereas standard relative
and absolute criteria do not have this property. For the analysis, the
iteration is modelled as a perturbed fixed point iteration and existing
analysis is extended to the nested case x=F(S(x)).
