Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 92375, 13 pages
doi:10.1155/JAMSA/2006/92375

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

Abstract

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.