Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 1, Pages 1-8
doi:10.1155/S1048953304302017

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

Abstract

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.