Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 1, Pages 1-8

Essential 𝒰cκ-type maps and Birkhoff-Kellogg theorems

R. 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, Ireland

Received 10 February 2003; Revised 15 September 2003

Copyright © 2004 R. P. Agarwal and Donal O'Regan. 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.


We present a new continuation theorem for 𝒰cκ-type maps. The analysis is elementary and relies on properties of retractions and fixed point theory for self-maps. Also we present some Birkhoff-Kellogg type theorems on invariant directions.