Abstract
Several new fixed point results are presented for set valued maps. The maps we discuss are either ofM * type or of regularly approximable type.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Ben-El-Mechaiekh, Fixed points for compact set-valued maps,Q. and A. in General Topology,10(1992), 153–156.
H. Ben-El-Mechaiekh and P.Deguire, Approachability and fixed points for non-convex set-valued maps,Jour. Math. Anal. Appl.,170(1992), 477–500.
H. Ben-El-Mechaiekh, P.Deguire and A.Granas, Points fixes et coincidences pour les applications multivoques (applications de Ky. Fan),C. R. Acad. Sc.,295(1982), 337–340.
H. Ben-El-Mechaiekh, P. Deguire and A.Granas, Points fixes et coincidences pour les applications multivoques II (applications de type Φ et Φ*),C. R. Acad. Sc.,295(1982), 381–384.
H. Ben-El-Mechaiekh, P.Deguire and A.Granas, Points fixes et coincidences pour les applications multivoques III (applications de typeM etM *),C. R. Acad. Sc.,305(1987), 381–384.
H. Ben-El-Mechaiekh and A.Idzik, A Leray-Schauder type theorem for approximable maps,Proc. Amer. Math. Soc.,122(1994), 105–109.
F. E. Browder, The fixed point theory of multivalued mappings in topological vector spaces,Math. Anal.,177(1968), 283–301.
J.Dugundji and A.Granas, Fixed point theory,Monografie Matematyczne, PWN, Warsaw, 1982.
M.Furi and P.Pera, A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals,Ann. Polon. Math.,47(1987), 331–346.
L.Gorniewicz, Topological approach to differential inclusions. Topological Methods in Diff. Eqns. and Inclusions (edited by A.Granas and M.Frigon), NATO ASI Series C,vol. 472,Kluwer Acad. Publ., Dordrecht, 1995, 129–190
L.Gorniewicz and M.Lassonde, On approximable multi-valued mappings, preprint, 1990.
A. Granas, On the Leray-Schauder alternative,Top. Methods in Nonlinear Anal.,2(1993), 225–231.
C.J.Himmelberg, Fixed points for compact multifunctions,J. Math. Anal. Appl.,38(1972), 205–207.
V. Klee, Leray-Schauder theory without local convexity,Math. Annalen,141(1960), 286–296.
E.Michael, Continuous selections,Ann. Math.,63(1956), 361–382.
R.D.Mauldin (ed.), The Scottish Book,Birkhauser, Boston, 1981.
D.O'Regan, Fixed point theory for compact upper semi-continuous or lower semicontinuous maps,Proc. Amer. Math. Soc., to appear.
A.J.B.Potter, An elementary version of the Leray-Schauder theorem,Jour. London Math. Soc.,5(1972), 414–416.
F. Treves, Topological vector spaces, distributions and kernels,Academic Press, New York, 1967.
E.Zeidler, Nonlinear functional analysis and its applications, Vol I,Springer Verlag, New York, 1986.
Author information
Authors and Affiliations
Additional information
47H10
Rights and permissions
About this article
Cite this article
O'Regan, D. Fixed points forM ⋆ and regularly approximable maps. Integr equ oper theory 28, 321–329 (1997). https://doi.org/10.1007/BF01294156
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01294156