Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 92375, 13 pages

Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: The projective limit approach

Ravi P. Agarwal1 and Donal O'Regan2

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland

Received 9 December 2005; Accepted 5 January 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.


We present a generalization of the cone compression and expansion results due to Krasnoselskii and Petryshyn for multivalued maps defined on a Fréchet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.