See also
Absolutely Continuous Function,
Bi-Lipschitz Map,
Contraction
Mapping,
Integer Lipschitz Height
Function,
Lipschitz Condition,
Lipschitz
Constant,
Lipschitz Extension Problem,
Lipschitz Isomorphism Problem,
Metric Embedding Distortion,
Metric
Space,
Nonexpansive Map,
Real
Lipschitz Height Function,
Uniform Rectifiability
Portions of this entry contributed by Todd
Rowland
Explore with Wolfram|Alpha
References
Gutev, V. "Lipschitz Extensions and Approximations." J. Math. Anal. Appl. 491, Article 124242, 2020. https://doi.org/10.1016/j.jmaa.2020.124242.Hunter,
J. K. "Lipschitz Functions." §3.A.1 in Notes on Partial Differential
Equations. p. 77, 2014. https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf.Referenced
on Wolfram|Alpha
Lipschitz Function
Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Lipschitz Function." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/LipschitzFunction.html
Subject classifications
between metric spaces
for which a constant 
satisfies
, where 
and 
are the respective metrics (Gutev
2020). In particular, a real-valued function 
on a subset 
of the real
numbers is Lipschitz if
, where 
is a constant independent
of 
and 
.
For example, a differentiable real-valued function on an interval with
a bounded first
derivative is Lipschitz by the mean-value theorem
(Hunter 2014, p. 77).
