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A Leray-Schauder type theorem for approximable maps: a simple proof
Author(s):
H.
Ben-El-Mechaiekh;
S.
Chebbi;
M.
Florenzano
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2345-2349.
MSC (1991):
Primary 47H04, 47H10, 54C60
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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:
- [B]
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- [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]
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- 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
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- S. Park, Fixed points of approximable maps, Proc. Amer. Math. Soc. 124 (1996), 3109-3114. MR 96m:47108
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- 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.
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- S. Reich, Fixed points in locally convex spaces, Mat. Z. 125 (1972), 17-31. MR 46:6110
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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:
10.1090/S0002-9939-98-04655-3
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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