Geodesic
A Note on a Theorem of Ky Fan
Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 513-515

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Fan ([2, Theorem 2]) has proved the following theorem:Let K be a nonempty compact convex set in a normed linear space X. For any continuous map f from K into X, there exists a point u∈K such that In this note, we prove that the above theorem is true for a continuous condensing map defined on a closed ball in a Banach space. We also prove that it is true for a continuous condensing map defined on a closed convex bounded subset of a Hilbert space. 
Lin, Tzu-Chu. A Note on a Theorem of Ky Fan. Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 513-515. doi: 10.4153/CMB-1979-067-x
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     title = {A {Note} on a {Theorem} of {Ky} {Fan}},
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