Fixed-point stability in the uniform metric
= Fixed-point stability in the uniform metric
{title2=$d(x_f,x_g)\leq d_\infty(f,g)/(1-q_f)$}
For two <contraction mappings> of a nonempty <complete metric space>, their <fixed points> obey $d(x_f,x_g)\leq q_fd(x_f,x_g)+d_\infty(f,g)$. Rearranging proves the displayed bound whenever the <uniform metric> is finite. It establishes continuity of the fixed-point map at each $f$ without assuming a contraction constant shared by all maps near $f$.