A Note on a Theorem of Ky Fan

Tzu-Chu Lin

doi:10.4153/CMB-1979-067-x

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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.

References

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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