Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 173-185
doi:10.1155/S1687182004403027
Continuation theory for general contractions in gauge spaces
Adela Chiş1
and Radu Precup2
1Department of Mathematics, Technical University of Cluj, Cluj-Napoca 400020, Romania
2Department of Applied Mathematics, Babeş-Bolyai University of Cluj, Cluj-Napoca 400084, Romania
Abstract
A continuation principle of Leray-Schauder type is presented for contractions with respect to a gauge structure depending on the homotopy parameter. The result involves the most general notion of a contractive map on a gauge space and in particular yields homotopy invariance results for several types of generalized contractions.