Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A Leray-Schauder type theorem
for approximable maps: a simple proof


Authors: H. Ben-El-Mechaiekh, S. Chebbi and M. Florenzano
Journal: Proc. Amer. Math. Soc. 126 (1998), 2345-2349
MSC (1991): Primary 47H04, 47H10, 54C60
DOI: https://doi.org/10.1090/S0002-9939-98-04655-3
MathSciNet review: 1476117
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present a simple and direct proof for a Leray-Schauder type alternative for a large class of condensing or compact set-valued maps containing convex as well as nonconvex maps.


References [Enhancements On Off] (What's this?)

  • [B] H. Bel El Mechaiekh, Continuous approximations of multifunctions, fixed points and coincidences, in Approximation and Optimization in the Carribean II, Proceedings of the Second International Conference on Approximation and Optimization in the Carribean, Florenzano et al. Eds., Verlag Peter Lang, Frankfurt, (1995), 69-97.
  • [BD] H. Ben-El-Mechaiekh and P. Deguire, Approachability and fixed points for non-convex set-valued maps, J. Math. Anal. Appl. 170 (1992), 477-500. MR 94a:54103
  • [BI] H. Bel-El-Mechaiekh and A. Idzik, A Leray-Schauder type theorem for approximable maps, Proc. Amer. Math. Soc. 122 (1994), 105-109. MR 94k:54074
  • [C] A. Cellina, A theorem on the approximation of compact multivalued mappings, Atti Accad. Naz. Lincei (8) 47 (1969), 429-433. MR 43:2676
  • [CF] S. Chebbi and M. Florenzano, Maximal elements and equilibria for condensing correspondences, Cahiers Eco-Math 95.18 (1995), CERMSEM, Université de Paris I, to appear in Nonlinear Analysis.
  • [DG] J. Dugundji and A. Granas, Fixed point theory I, Monografie Math. 61, PWN, Warszawa, 1982. MR 83j:54038
  • [GGK] L. Górniewicz, A. Granas and W. Kryszewski, Sur la methode de l'homotopie dans la theorie des points fixes pour les applications multivoques, Partie I: Transversalité topologique, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), 489-492; Partie II: L'indice dans les ANRs compacts, 308 (1989), 449-452. MR 90g:55002; MR 90j:55004
  • [K] G. Köthe, Topological Vector Spaces I, Springer-Verlag, New York Inc., 1969. MR 40:1750
  • [P] S. Park, Fixed points of approximable maps, Proc. Amer. Math. Soc. 124 (1996), 3109-3114. MR 96m:47108
  • [PF] W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1-25.
  • [R1] S. Reich, Fixed points in locally convex spaces, Mat. Z. 125 (1972), 17-31. MR 46:6110
  • [R2] S. Reich, Fixed points of condensing functions, J. Math. Anal. Appl. 41 (1973), 460-467. MR 48:971
  • [R3] S. Reich, A remark on set-valued mapppings that satisfy the Leray-Schauder condition I, II, Atti Accad. Naz. Lincei 61 (1976), 193-194; 66 (1979), 1-2.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H04, 47H10, 54C60

Retrieve articles in all journals with MSC (1991): 47H04, 47H10, 54C60


Additional Information

H. Ben-El-Mechaiekh
Affiliation: Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1
Address at time of publication: Department of Mathematics, The American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Email: hmechaiekh@aus.ac.ae

S. Chebbi
Affiliation: CERMSEM, Université de Paris I, 106-112 Bd de l’Hopital, 75013 Paris, France
Email: chebbi@univ-parisl.fr

M. Florenzano
Affiliation: CNRS-CEPREMAP, 140 rue du Chevaleret, 75013 Paris, France
Email: monique.florenzano@cepremap.cnrs.fr

DOI: https://doi.org/10.1090/S0002-9939-98-04655-3
Keywords: Leray-Schauder alternative, approximable set-valued maps, condensing, compact
Received by editor(s): August 12, 1996
Received by editor(s) in revised form: January 16, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society