Fixed Point Theory and Applications
Volume 2005 (2005), Issue 1, Pages 1-10

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

Copyright © 2005 Ravi P. Agarwal et al. 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.


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.