A short proof of Fan’s fixed point theorem
HTML articles powered by AMS MathViewer
- by Frode Terkelsen PDF
- Proc. Amer. Math. Soc. 42 (1974), 643-644 Request permission
Abstract:
Fan’s fixed point theorem for multivalued functions in locally convex spaces is proved by means of Brouwer’s fixed point theorem and the concept of a partition of unity.References
- Felix E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283–301. MR 229101, DOI 10.1007/BF01350721
- Ky. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121–126. MR 47317, DOI 10.1073/pnas.38.2.121
- Shizuo Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Math. J. 8 (1941), 457–459. MR 4776
- A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767–776 (German). MR 1513031, DOI 10.1007/BF01472256
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 643-644
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0333857-8
- MathSciNet review: 0333857