A nonexpansive map 
between metric spaces is a map
satisfying 
for all 
.
For normed spaces, this condition is 
. It permits equality and therefore
includes the identity map.
Nonexpansive Map
See also
Banach Space, Map Fixed Point, Metric Space, Reflexive SpaceExplore with Wolfram|Alpha
References
Naor, A. Metric Embeddings and Lipschitz Extensions. Lecture notes taken by A. Eskenazis, spring 2015. https://web.math.princeton.edu/~naor/homepage%20files/embeddings_extensions.pdf.Cite this as:
Weisstein, Eric W. "Nonexpansive Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonexpansiveMap.html