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Let be a closed convex subset of a Banach Space and assume there exists a continuous Map
sending
to a countably compact subset
of
. Then
has fixed points.
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.