Definition:Uniform Contraction Mapping

Definition
Let $M$ and $N$ be metric spaces.

Let $f : M \times N \to M$ be a mapping.

Then $f$ is a uniform contraction there exists $K<1$ such that for all $x,y\in M$ and $t\in N$:
 * $d(f(x,t), f(y,t)) \leq K\cdot d(x,y)$.

Also see

 * Uniform Contraction Mapping Theorem
 * Definition:Uniform Lipschitz Condition