Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 1, Pages 1-10
doi:10.1155/FPTA.2005.1

A Leray-Schauder alternative for weakly-strongly sequentially continuous weakly compact maps

Ravi P. Agarwal,1 Donal O'Regan,2 and Xinzhi Liu3

 1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland
3Department of Applied Mathematics, University of Waterloo, ON, N2L 3G1, Canada
Received 23 June 2004; Revised 17 November 2004

Abstract

A new applicable Leray-Schauder alternative is presented for weakly-strongly sequentially continuous maps. This result is then used to establish a general existence principle for operator equations.