A general coincidence theorem on contractible spaces

Park, Sehie; Jeong, Kwang

doi:10.1090/S0002-9939-96-03513-7

A general coincidence theorem on contractible spaces
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by Sehie Park and Kwang Sik Jeong PDF

Proc. Amer. Math. Soc. 124 (1996), 3203-3206 Request permission

Abstract:

We obtain a general coincidence theorem for multifunctions in very large classes defined on contractible spaces. Our theorem generalizes a recent result due to Tarafdar and Yuan (1994) and many other earlier works including the Fan-Browder fixed point theorem.

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
H. Ben-El-Mechaiekh and A. Idzik, A Leray-Schauder type theorem for approximable maps, Proc. Amer. Math. Soc. 122 (1994), no. 1, 105–109. MR 1212281, DOI 10.1090/S0002-9939-1994-1212281-2
Ky Fan, A generalization of Tychonoff’s fixed point theorem, Math. Ann. 142 (1960/61), 305–310. MR 131268, DOI 10.1007/BF01353421
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
Marc Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), no. 1, 151–201. MR 721236, DOI 10.1016/0022-247X(83)90244-5
Sehie Park, On minimax inequalities on spaces having certain contractible subsets, Bull. Austral. Math. Soc. 47 (1993), no. 1, 25–40. MR 1201420, DOI 10.1017/S0004972700012235
Sehie Park, Coincidences of composites of admissible u.s.c. maps and applications, C. R. Math. Rep. Acad. Sci. Canada 15 (1993), no. 4, 125–130. MR 1240816
Sehie Park, Fixed point theory of multifunctions in topological vector spaces. II, J. Korean Math. Soc. 30 (1993), no. 2, 413–431. MR 1239332
Sehie Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), no. 3, 493–519. MR 1297433
—, Generalized Leray-Schauder principles for compact admissible multifunctions, Top. Meth. Nonlinear Anal. 5 (1995), 271–277.
S. Park and H. Kim, Admissible classes of multifunctions on generalized convex spaces, Proc. Coll. Natur. Sci., Seoul Nat. U. 18 (1993), 1–21.
—, Coincidences of composites of u.s.c. maps on $H$-spaces and applications, J. Korean Math. Soc. 32 (1995), 251–264.
Sehie Park, S. P. Singh, and Bruce Watson, Some fixed point theorems for composites of acyclic maps, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1151–1158. MR 1189547, DOI 10.1090/S0002-9939-1994-1189547-8
E. Tarafdar and Xian-Zhi Yuan, A remark on coincidence theorems, Proc. Amer. Math. Soc. 122 (1994), no. 3, 957–959. MR 1260181, DOI 10.1090/S0002-9939-1994-1260181-4