A remark on coincidence theorems

Tarafdar, E.; Yuan, Xian-Zhi

doi:10.1090/S0002-9939-1994-1260181-4

A remark on coincidence theorems
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by E. Tarafdar and Xian-Zhi Yuan PDF

Proc. Amer. Math. Soc. 122 (1994), 957-959 Request permission

Abstract:

Using a different approach, we prove a general coincidence theorem of multivalued mappings which have contractible values in non-convex setting.

References

Jean-Pierre Aubin, Mathematical methods of game and economic theory, Studies in Mathematics and its Applications, vol. 7, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 556865
Felix E. Browder, Coincidence theorems, minimax theorems, and variational inequalities, Conference in modern analysis and probability (New Haven, Conn., 1982) Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 67–80. MR 737389, DOI 10.1090/conm/026/737389
Samuel Eilenberg and Deane Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214–222. MR 16676, DOI 10.2307/2371832
L. Górniewicz, A Lefschetz-type fixed point theorem, Fund. Math. 88 (1975), no. 2, 103–115. MR 391062, DOI 10.4064/fm-88-2-103-115
Andrzej Granas and Fon Che Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. (9) 65 (1986), no. 2, 119–148. MR 867668
Chung Wei Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), no. 1, 73–77. MR 569411, DOI 10.1007/BF01349255
Charles D. Horvath, Convexité généralisée et applications, Méthodes topologiques en analyse convexe (Montreal, PQ, 1986) Sém. Math. Sup., vol. 110, Presses Univ. Montréal, Montreal, QC, 1990, pp. 79–99 (French). MR 1060738
Charles D. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl. 156 (1991), no. 2, 341–357. MR 1103017, DOI 10.1016/0022-247X(91)90402-L
Shizuo Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Math. J. 8 (1941), 457–459. MR 4776
H. Komiya, Coincidence theorem and saddle point theorem, Proc. Amer. Math. Soc. 96 (1986), no. 4, 599–602. MR 826487, DOI 10.1090/S0002-9939-1986-0826487-0
Naoki Shioji, A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, Proc. Amer. Math. Soc. 111 (1991), no. 1, 187–195. MR 1045601, DOI 10.1090/S0002-9939-1991-1045601-X

Contributions to nonlinear analysis