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A fixed point theorem for multifunctions in a locally convex space. (English) Zbl 0272.54037


MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54C60 Set-valued maps in general topology
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References:

[1] Felix E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283 – 301. · Zbl 0176.45204 · doi:10.1007/BF01350721
[2] Ky. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 121 – 126. · Zbl 0047.35103
[3] Ky Fan, A generalization of Tychonoff’s fixed point theorem, Math. Ann. 142 (1960/1961), 305 – 310. · Zbl 0093.36701 · doi:10.1007/BF01353421
[4] I. L. Glicksberg, A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170 – 174. · Zbl 0046.12103
[5] C. J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205 – 207. · Zbl 0204.23104 · doi:10.1016/0022-247X(72)90128-X
[6] Shizuo Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Math. J. 8 (1941), 457 – 459. · Zbl 0061.40304
[7] A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767 – 776 (German). · Zbl 0012.30803 · doi:10.1007/BF01472256
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