Continuity of the fixed-point assignment
= Continuity of the fixed-point assignment
{title2=$d(\tau(f),\tau(g))\le d_\infty(f,g)/(1-q_f)$}
For <contraction mappings> $f,g$, compare their <fixed points> using $f$ on both arguments, then bound the change from $f$ to $g$ by the <uniform metric>. The resulting inequality gives the displayed estimate. Continuity at $f$ only needs its own contraction constant $q_f<1$, even if nearby maps have constants approaching one.