A Note on a Theorem of Ky Fan

Canadian Mathematical Bulletin - Tập 22 Số 4 - Trang 513-515 - 1979
Tzu-Chu Lin1
1Department of Mathematics, University of Iowa, Iowa City, Iowa, 52242

Tóm tắt

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 thatIn 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.

Từ khóa


Tài liệu tham khảo

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10.4064/fm-15-1-301-309

10.1090/S0002-9939-1959-0105008-8

10.1007/BF01110225

10.1215/S0012-7094-58-02550-X

Nussbaum, 1969, The fixed point index and fixed point theorems for k-set-contractions, doctoral dissertation,

10.1007/BF01076087

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Canadian Mathematical Bulletin

Tập 22 Số 4

513-515

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