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, Lipschitz Constant, Lipschitz Function, Map Fixed Point, Metric 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