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Fixed point theorems for condensing multivalued mappings on a locally convex topological space

Published online by Cambridge University Press:  17 April 2009

E. Tarafdar  and
R. Výborný
E. Tarafdar
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
R. Výborný
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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Abstract

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A general definition for a measure of nonprecompactness for bounded subsets of a locally convex linear topological space is given. Fixed point theorems for condensing multivalued mappings have been proved. These fixed point theorems are further generalizations of Kakutani's fixed point theorems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 161 - 170
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Browder, Felix E., “On a generalization of the Schauder fixed point theorem”, Duke Math. J. 26 (1959), 291–303.CrossRefGoogle Scholar
[2]Daneš, Josef, “Some fixed point theorems”, Comment. Math. Univ. Carolinae 9 (1968), 223–235.Google Scholar
[3]Darbo, Gabriele, “Punti uniti in trasformazioni a codominio non compatto”, Rend. Sent. Mat. Univ. Padova 24 (1955), 84–92.Google Scholar
[4]Ky, Fan, “Fixed-point and minimax theorems in locally convex topological linear spaces”, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121–126.Google Scholar
[5]Glicksberg, I.L., “A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points”, Proc. Amer. Math. Soc., 3 (1952), 170–174.Google Scholar
[6]Himmelberg, C.J., Porter, J.R. and van Vleck, F.S., “Fixed point theorems for condensing multifunctions”, Proc. Amer. Math. Soc. 23 (1969), 635–614.CrossRefGoogle Scholar
[7]Kakutani, Shizuo, “A generalization of Brouwer's fixed point theorem”, Duke Math. J. 8 (1914), 457–459.Google Scholar
[8]Kuratowski, K., Topology, Vol. I (New edition, revised and augmented. Translated by Jaworowski, J.. Academic Press, New York, London; Państwowe Wydawnictwo Naukowe, Warsaw; 1966).Google Scholar
[9]Лифшиц, Е.А., Садовсний, Б.Н. [E.A. Lifšic, B.N. Sadovskiĭ], “Теорема о неподвижной тоцке Для обобщенно уплотндющих оиераторов” [A fixed-point theorem for generalized condensing operators], Dokl. Akad. Nauk SSSX 183 (1968), 278–279; English translation: Soviet Math. Dokl. 9 (1968), 1370–1372.Google ScholarPubMed
[10]Reinermann, Jochen, “Fixpunktsätze vom Krasnoselski-Typ”, Math. Z. 119 (1971), 339–344.CrossRefGoogle Scholar
[11]Sadovskiĭ, B.N., “A fixed-point principle”, Functional Anal. Appl. 1 (1967), 151–153.CrossRefGoogle Scholar
[12]Schauder, J., “Der Fixpunktsatz in Funktionalräumen”, Studio Math. 2 (1930), 171–180.CrossRefGoogle Scholar
[13]Stallbohm, Volker, “Fixpunkte nichtexpansiver Atbildungen, Fixpunkte kondensierender Abbildungen, Fredholm'sche Sätze linearer kondensierender Abbildungen”, (Rheinisch-Westfälische Technische Hochschule Aachen, Dr. Nat. Dissertation, 1973).Google Scholar
[14]Tychonoff, A., “Ein Fixpunktsatz”, Math. Ann. 111 (1935), 767–776.CrossRefGoogle Scholar