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Continuous selections and fixed points of multi-valued mappings on noncompact or nonmetrizable spaces

Authors: Lai-Jiu Lin, Ngai-Ching Wong and Zenn-Tsuen Yu
Journal: Proc. Amer. Math. Soc. 133 (2005), 3421-3427
MSC (2000): Primary 54C65, 46H10, 54H25
Published electronically: June 20, 2005
MathSciNet review: 2161168
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Abstract: In this paper, we obtain several new continuous selection theorems for multi-valued mappings on completely regular spaces and fixed point theorems for multi-valued maps on nonmetrizable spaces. They, in particular, provide a partial solution of a conjecture of X. Wu.

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  • 1. R. Agarwal and D. O'Regan, Fixed point theory for maps with lower semicontinuous selections and equilibrium theory for abstract economies, J. Nonlinear and Convex Analysis, 2 (2001), 31-46. MR 1828157 (2002m:49025)
  • 2. H. Ben-El-Mechaiekh, The coincidence problem for compositions of set-valued maps, Bull. Austral Math. Soc., 41 (1990), 421-434. MR 1071044 (91h:47060)
  • 3. H. Ben-El-Mechaiekh, Fixed points for compact set-valued maps, Questions Answers Gen. Topology, 10(1992), 153-156. MR 1180474
  • 4. F. E. Browder, A new generation of the Schauder fixed point theorem, Math. Ann., 174 (1967), 285-290. MR 0223944 (36:6991)
  • 5. F. E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann., 177 (1968), 283-301. MR 0229101 (37:4679)
  • 6. P. Cubiotti, Some remarks on fixed points of lower semicontinuous multifunctions, J. Math. Anal. Appl., 174 (1993), 407-412. MR 1215621 (94c:47081)
  • 7. F. Deutsch and P. Kenderov, Continuous selections and approximate selection for set-valued mappings and applications to metric projections, SIAM J. Math. Anal., 14 (1983), 185-194. MR 0686245 (84c:54026)
  • 8. X. P. Ding, W. K. Kim and K. K. Tan, A selection theorem and its applications, Bull. Austral. Math. Soc., 46 (1992), 205-212. MR 1183778 (93g:47072)
  • 9. A. Granas, Points fixes pour les applications compactes: espaces de Lefschetz et la théorie de l'indice, Séminaire de Mathématiques Supérieures 68, Presses de l'Université de Montréal, Montreal, Que., 1980. MR 0569745 (81i:55002)
  • 10. C. J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl., 38 (1972), 205-207. MR 0303368 (46:2505)
  • 11. C. D. Horvath, Extension and selection theorems in topological vector spaces with a generalized convexity structure, Ann. Fac. Sci., Toulouse 2, (1993), 253-269. MR 1253391 (94i:54043)
  • 12. S. Park, Continuous selection theorems in generalized convex spaces, Numer. Funct. Anal. Optim., 25 (1999), 567-583. MR 1704961 (2000e:54014)
  • 13. S. Park, The Knaster-Kuratowski-Mazurkiewicz Theorem and almost fixed points, Top. Methods in Nonlinear Anal., 16 (2000), 195-200. MR 1805047 (2001m:47118)
  • 14. G. Tian, Fixed point theorems for mappings with noncompact and nonconvex domains, J. Math. Anal. Appl., 158 (1991), 161-167. MR 1113407 (92e:47110)
  • 15. X. Wu, A new fixed point theorem and its applications, Proc. Amer. Math. Soc., 125 (1997), 1779-1783. MR 1397000 (97h:90014)
  • 16. X. Wu and S. Shen, A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications, J. Math. Anal. Appl., 197 (1996), 61-74. MR 1371276 (97a:47085)
  • 17. N. C. Yannelis and N. D. Prabhakar, Existence of maximal elements and equilibria in linear topological spaces, J. Math. Economics, 12 (1983), 233-245. MR 0743037 (87h:90061a)
  • 18. Z. T. Yu and L. J. Lin, Continuous selection and fixed point theorems, Nonlinear Anal., 52 (2003), 445-455. MR 1937632 (2003g:54040)
  • 19. G. X. Z. Yuan, G. Isac, K. K. Tan, and J. Yu, The study of minimax inequalities, abstract economics and applications to variational inequalities and Nash equilibria, Acta Applicandae Mathematicae, 54 (1998), 135-166. MR 1660931 (99j:49018)
  • 20. X. Zheng, Approximate selection theorems and their applications, J. Math. Anal. Appl., 212 (1997), 88-97. MR 1460186 (98h:90118)

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Additional Information

Lai-Jiu Lin
Affiliation: Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

Ngai-Ching Wong
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, and National Center for Theoretical Sciences, Kaohsiung, 80424, Taiwan

Zenn-Tsuen Yu
Affiliation: Department of Electrical Engineering, Nan-Kai Institute of Technology, Nantour 542, Taiwan

Keywords: Multi-valued mappings, continuous selections, fixed points
Received by editor(s): July 17, 2003
Published electronically: June 20, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society

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