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


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