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Schauder Fixed Point Theorem


Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.


See also

Map Fixed Point

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References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 543, 1980.Schauder, J. "Der Fixpunktsatz in Funktionalräumen." Studia Math. 2, 171-180, 1930.Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.

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Schauder Fixed Point Theorem

Cite this as:

Weisstein, Eric W. "Schauder Fixed Point Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchauderFixedPointTheorem.html

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