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. Agarwal,1 Jewgeni H. Dshalalow,1 and Donal O'Regan2

 1Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne 32901–6975, FL, USA
2Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland
Received 17 May 2005

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.