Abstract
New Leray-Schauder results are presented for multivalued
contractions defined on subsets of a Fréchet space
Open Access
Leray-Schauder results for multivalued nonlinear contractions defined on closed subsets of a Fréchet space
Received09 Dec 2005
Revised21 Feb 2006
Accepted25 Apr 2006
Published29 Aug 2006
References
R. P. Agarwal, J. Dshalalow, and D. O'Regan, “Fixed point and homotopy results for generalized contractive maps of Reich type,” Applicable Analysis, vol. 82, no. 4, pp. 329–350, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. P. Agarwal and D. O'Regan, “Various homotopy results for generalized single valued contractions on Fréchet spaces,” Journal of Concrete and Applicable Mathematics, vol. 1, no. 2, pp. 101–111, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Frigon, “Fixed point results for generalized contractions in gauge spaces and applications,” Proceedings of the American Mathematical Society, vol. 128, no. 10, pp. 2957–2965, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Frigon, “Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 9, no. 1, pp. 23–37, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetL. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1964.
View at: Google ScholarD. O'Regan, “Fixed point theorems for nonlinear operators,” Journal of Mathematical Analysis and Applications, vol. 202, no. 2, pp. 413–432, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.