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On a fixed point theorem of Ky Fan. (English) Zbl 1027.47058
The authors extend a classical fixed point theorem (in a generalized sense) by Ky Fan [Math. Z. 112, 234-240 (1969; Zbl 0185.39503)].

MSC:
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Fan Ky, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 1969, 112:234–240 · Zbl 0185.39503 · doi:10.1007/BF01110225
[2] Beer G., Pai D. V., Proximal maps, prox maps and coincidence points, Numer. Funct. Anal. Optimiz., 1990, 11:429–448 · Zbl 0726.41035 · doi:10.1080/01630569008816382
[3] Ding X. P., Tan K. K., A set-valued generalization of Fan’s best approximation theorem, Canad. J. Math., 1992, 44:784–796 · Zbl 0761.47037 · doi:10.4153/CJM-1992-046-9
[4] Lin T. C., A note on a theorem of Ky Fan, Canad. Math. Bulletin, 1979, 22:513–515 · Zbl 0429.47019 · doi:10.4153/CMB-1979-067-x
[5] Lin T. C., Yen C. L., Applications of the proximity map to fixed point theorems in Hilbert space, J. Approx. Theory, 1988, 52:141–148 · Zbl 0643.47053 · doi:10.1016/0021-9045(88)90053-6
[6] Reich S., Approximate selections, best approximations, fixed points, and invariant sets, J. Math. Anal. Appl., 1978, 62:104–113 · Zbl 0375.47031 · doi:10.1016/0022-247X(78)90222-6
[7] Sehgal V. M., A simple proof of a theorem of Ky Fan, Proc. Amer. Math. Soc., 1977, 63:368–369 · Zbl 0355.47038
[8] Sehgal V. M., Singh S. P., A generalization to multifunctions of Fan’s best approximation, Proc. Amer. Math. Soc., 1988, 102:534–537 · Zbl 0672.47043
[9] Sehgal V. M., Singh S. P., Watson B., Best approximation and fixed point theorems, Bull. Allahabad Math. Soc., 1991, 6:11–27 · Zbl 1097.47521
[10] Singh S. P., Watson B., Proximity maps and fixed points, J. Approx. Theory, 1983, 28:72–76 · Zbl 0518.47040 · doi:10.1016/0021-9045(83)90069-2
[11] Waters C. W., Some fixed point theorems for radial contractions, nonexpansive and set-valued mappings, Ph. D. Thesis, University of Wyoming, U. S. A., 1994
[12] Kakutani S., A generalization of Brouwer’s fixed point theorem, Duke Math. J., 1941, 8:457–459 · Zbl 0061.40304 · doi:10.1215/S0012-7094-41-00838-4
[13] Fan Ky, Fixed points and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A., 1952, 38:121–126 · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121
[14] Rådström H., An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc., 1952, 3:165–169 · Zbl 0046.33304
[15] Michael E., Continuous selections I, Ann. Math., 1956, 63:361–382 · Zbl 0071.15902 · doi:10.2307/1969615
[16] Hu S., Papageorgiou N. S., Handbook of multivalued analysis, Vol. I, Kluwer, Dordrecht, 1997 · Zbl 0887.47001
[17] Schwartz J. T., Nonlinear functional analysis, Gordon and Breach, New York, 1969
[18] Hukuhara M., Sur l’application semi-continue dont la valeur est un compact convexe, Funkcial. Ekvac., 1967, 10:43–66 · Zbl 0155.19402
[19] De Blasi F. S., Characterizations of certain classes of semicontinuous multifunctions by continuous approximations, J. Math. Anal. Appl., 1985, 106:1–18 · Zbl 0574.54012 · doi:10.1016/0022-247X(85)90126-X
[20] Dunford N., Schwartz J. T., Linear operators, Part I, J. Wiley, New York, 1958
[21] De Blasi F. S., Georgiev P. G., Hukuhara topological degree for non compact valued multifunctions, Centro V. Volterra, Università di Roma ”Tor Vergata”, preprint No. 377, 1999
[22] Cellina A., A theorem on the approximation of compact multivalued mappings, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 1969, 8:149–153 · Zbl 0194.44704
[23] Borisovitch Y. G., Gel’man B. D., Mukhamadiev E., Obukhovskii V. V., On the rotation of multivalued vector fields, Dokl. Akad. Nauk SSSR, 1969, 187:971–973
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