International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2775-2782
doi:10.1155/IJMMS.2005.2775
Fixed point theory for Mönch-type maps defined on closed subsets of Fréchet spaces: the projective limit approach
Ravi P. Agarwal1
, Jewgeni H. Dshalalow1
and Donal O'Regan3
1Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
3Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland
Abstract
New Leray-Schauder alternatives are presented for Mönch-type maps defined between Fréchet spaces. The proof relies on viewing a Fréchet space as the projective limit of a sequence of Banach spaces.