Definition:Uniform Contraction Mapping

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Definition

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

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


Then $f$ is a uniform contraction if and only if there exists $K<1$ such that for all $x,y\in M$ and $t\in N$:

$d(f(x,t), f(y,t)) \leq K\cdot d(x,y)$.


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