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
Received 9 March 2004; Revised 30 April 2004

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.