Spaces and maps approximation and fixed points

Journal of Computational and Applied Mathematics

Volumn 113, Issue 1, 2000, Pages 283-308

  Ben El Mechaiekh, Hichem ^a  

^a BROCK UNIVERSITY   (Canada)

Author keywords

Approachable set valued maps; AR and ANR; Contractibility; Fixed points; Neighborhood extension spaces; Polyhedra; Topological convexity structures; Trivial shape

Indexed keywords

SET THEORY; TOPOLOGY;

SET-VALUED MAPS;

APPROXIMATION THEORY;

EID: 0033890294     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00262-9     Document Type: Article

References (41)

1. H. Ben-El-Mechaiekh, Continuous approximations of multifunctions, fixed points and coincidences, in: M. Florenzano et al. (Eds.), Approximation and Optimization in the Caribbean II, Verlag Peter Lang 8, Frankfurt, 1995, pp. 67-97.
2. H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano, J.V. Llinares, Abstract convexities and fixed points, J. Math. Anal. Appl. 222 (1998) 138-150.
3. H. Ben-El-Mechaiekh, P. Deguire, Approachability and fixed points for non-convex set-valued maps, J. Math. Anal. Appl. 170 (1992) 477-500.
4. H. Ben-El-Mechaiekh, G. Isac, Generalized multivalued variational inequalities, in: O. Letho, T.M. Rassias (Eds.), Topology and Analysis, Volume dedicated to Professor S. Stoilow, C. Andreian-Cazacu, World Scientific, Singapore, 1998, pp. 115-142.
5. R. Bielawski, Simplicial convexity and its applications, J. Math Anal. Appl. 127 (1987) 155-171.
6. K. Borsuk, Theory of Retracts, Monografie Matematyczne, Polish Scientific Publishers, Warszawa, 1967.
7. L.E.J. Brouwer, Uber ein eindeutige, stetige transformationen von flachen in sich, Math. Anal. 69 (1910) 176-180.
8. R.F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, IL, 1971.
9. A. Cellina, A theorem on the approximation of compact multivalued mappings, Atti Acccad. Naz. Lincei Rend. 8 (1969) 149-153.
10. M.H. Clapp, On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971) 117-130.
11. J. Dungundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951) 353-367.
12. J. Dugundji, Topology, Allyn and Bacon Series in Advanced Mathematics, Boston, 1966.
13. J. Dugundji, Modified Vietoris theorems for homotopy, Fund. Math. LXVI (1970) 223-235.
14. J. Dugundji, A. Granas, Fixed Point Theory I, Monografie Matematyczne, Polish Scientific Publishers, Warszawa, 1982.
15. K. Fan, Fixed point and minimax theorems in locally convex topological linear spaces, Proc. Natl. Acad. Sci. USA 38 (1952) 121-126.
16. G. Gabor, Fixed points of set-valued maps with closed proximally ∞-connected values, Discussiones Math. Differential Inclusions 15 (1995) 163-185.
17. G. Gauthier, La théorie des rétracts approximatifs et le théorème des points fixes de Lefschetz, Dissertationes Math. CCXVII, Warszawa, 1983.
18. L. Gorniewicz, A. Granas, W. Kryszewski, On the homotopy method in the fixed point index theory for multivalued mappings of compact ANR-s, J. Math Anal. Appl. 161 (1991) 457-473.
19. A. Granas, Points fixes pour les applications compactes: espaces de Lefschetz et la théorie de l'indice, vol. 68, Les Presses de l'Université de Montréal, 1980.
20. C.J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972) 205-207.
21. C.D. Horvath, Contractiblity and generalized convexity, J. Math. Anal. Appl. 156 (1991) 341-357.
22. C.D. Horvath, Extension and selection theorems in topological spaces with a generalized convexity structure, Ann. Fac. Sci. Toulouse 2 (2) (1993) 253-269.
23. C.D. Horvath, J.V. Llinares, Maximal elements and fixed points for binary relations on topological ordered spaces, J. Math. Economics 25 (1996) 291-306.
24. G. Isac, On the solvability of multivalued complementarity problem: a topological method, preprint, 1999.
25. S. Kakutani, A generalization of the Brouwer's fixed point theorem, Duke Math. J. 8 (1941) 457-459.
26. V. Klee, Leray-Schauder theory without local convexity, Math. Ann. 141 (1960) 286-296.
27. C. Kuratowski, Sur un théorème fondamental concernant le nerf d'un recouvrement d'un système d'ensembles, Fund. Math. 20 (1933) 191-196.
28. A. Mas Colell, A note on a theorem of F. Browder, Math. Programm. 6 (1974) 229-233.
29. J.R. Munkres, Elements of Algebraic Topology, Addison-Wesley, Reading, MA, 1984.
30. D. O'Regan, Generalized multivalued quasi variational inequalities, preprint.
31. S. Park, Eighty years of the Brouwer fixed point theorem, in: Antipodal Points and Fixed Points, RIMGARC Lecture Notes, vol. 28, Seoul National University, 1995.
32. S. Park, Fixed points of approximable maps, Proc. Amer. Math. Soc. 124 (1996) 3109-3114.
33. S. Park, Remarks on a fixed point problem of Ben-El-Mechaiekh, preprint, 1998.
34. S. Park, Some topological versions of the Fan-Browder fixed point theorem, preprint, 1998.
35. S. Park, H. Kim, Admissible class of multifunctions on generalized convex spaces, Proc. Coll. Natur. Sci. SNU 18 (1993) 1-21.
36. J. Schauder, Der fixpunktsatz in funktionalraumen, Studia Math. 2 (1930) 171-180.
37. E. Spanier, Algebraic Topology, Series in Higher Math., McGraw-Hill, New York, 1966.
38. E. Tarafdar, Fixed point theorems in locally H-convex uniform spaces, Nonlinear Anal. TMA 29 (1997) 971-978.
39. A. Tychonoff, Ein fixpunktsatz, Math. Ann. 111 (1935) 767-776.
40. J. Van Mill, Infinite Dimensional Topology, North-Holland, Amsterdam, 1989.
41. X-Z. Yuan, Fixed points of upper semicontinuous mappings in locally G-convex spaces, preprint, 1998.