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A fixed-point theorem for weakly condensing operators

Published online by Cambridge University Press:  14 November 2011

Donal O'Regan
Donal O'Regan
Affiliation:
Department of Mathematics, University College Galway, Galway, Ireland
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Extract

A new fixed-point theorem is presented for weakly condensing operators. Existence is then established for the nonlinear abstract operator y = Ny.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 391 - 398
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Adams, R.. Sobolei- Spaces (New York: Academic Press, 1975).Google Scholar
2Banas, J. and Goebel, K.. Measures of Noncompactness in Banach Spaces (New York: Marcel Dckker, 1980).Google Scholar
3Brooks, J. K. and Dinclueanu, N.. Weak compactness in spaces of Bochner integrable functions and applications. Adv. Math. 24 (1977), 172–88.CrossRefGoogle Scholar
4Conway, J. B.. A Course in Functional Analysis (Berlin: Springer. 1990).Google Scholar
5Corduncanu, C.. Integral Equations and Applications (New York: Cambridge University Press. 1991).CrossRefGoogle Scholar
6Corduncanu, C.. Abstract Volterra equations and weak topologies. In Delay Differential Equations and Dynamical Systems, eds Busenberg, S. and Martelli, M., Lecture Notes in Mathematics1475. 110–16 (Berlin, Springer. 1991).CrossRefGoogle Scholar
7DeBlasi, F. S.. On a property of the unit sphere in Banach spaces. Bull. Math. Soc. Sci. Math. R-S. Roumanie 21 (1977), 259–62.Google Scholar
8Diestcl, J. and Uhr, J. J. Jr. Vector Measures, Mathematical Surveys 15 (Providence, Rl: American Mathematical Society. 1977).CrossRefGoogle Scholar
9Dugundji, J. and Granas, A.. Fixed Point Theory. Monografic Matematyczne (Warsaw: PWN, 1982).Google Scholar
10Dunford, N. and Schwartz, J. T., Linear Operators (New York: WileyImcrscience. 1958).Google Scholar
11iimmanuele, G.. Measures of weak noncompactness and fixed point theorems. Bull Math. Soc.Sci. Math- R. S. Roumanie 25 (1981). 353–8.Google Scholar
12L-ngelking, R.. General Topology (Berlin: Heldermann, 1989).Google Scholar
13Faulkner, G. D.. On the nonexistence of weak solutions to abstract differential equations in nonreflexive spaces. Nonlinear Anal. 2 (1978). 505–8.CrossRefGoogle Scholar
14Kothe, G.. Topological Vector Spaces I(New York. Springer. 1983).CrossRefGoogle Scholar
15Lakshmikantham, V. and Leela, S.. Differential and Integral Inequalities, Vols I and II (New York: Academic Press. 1969).Google Scholar
16Lakshmikantham, V. and Lecla, S.. Nonlinear Differential Equations in Abstract Spaces (Oxford: Pergamon Press. 1981).Google Scholar
17Nagumo, M.. Degree of mapping in convex linear topological spaces, Amer. J. Math. 73 (1951), 497–511.CrossRefGoogle Scholar
18O'Regan, D.. Weak and strong topologies and integral equations in Banach spaces. Ann. Poion. Math. 61 (1995), 245–60.CrossRefGoogle Scholar
19Pruszko, T.. Some Applications of the Topologicai Degree Theory to Multi Valued Boundary Value Problems.Dissertationes Math. 229 (Warszawa: Polish Academy of Sciences. 1984).Google Scholar
20Yosida, K.. hunetional Analysis (Berlin: Springer, 1971).Google Scholar
21Dcimling, K., Nonlinear Functional Analysis (Springer Verlag. 1985).CrossRefGoogle Scholar