International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 43635, 8 pages

Leray-Schauder results for multivalued nonlinear contractions defined on closed subsets of a Fréchet space

Ravi P. Agarwal1 and Donal O'Regan2

1Department of Mathematical Science, Florida Institute of Technology, Melbourne 32901, FL, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland

Received 9 December 2005; Revised 21 February 2006; Accepted 25 April 2006

Copyright © 2006 Ravi P. Agarwal and Donal O'Regan. 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.


New Leray-Schauder results are presented for multivalued contractions defined on subsets of a Fréchet space E. The proof relies on fixed point results in Banach spaces and on viewing E as the projective limit of a sequence of Banach spaces.