Let 
be a contraction mapping from a closed subset 
of a Banach space 
into 
. Then there exists a unique 
such that 
.
Banach Fixed Point Theorem
See also
Fixed Point TheoremExplore with Wolfram|Alpha
References
Debnath, L. and Mikusiński, P. Introduction to Hilbert Spaces with Applications. San Diego, CA: Academic Press, 1990.Referenced on Wolfram|Alpha
Banach Fixed Point TheoremCite this as:
Weisstein, Eric W. "Banach Fixed Point Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BanachFixedPointTheorem.html