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

Copyright © 2004 Hindawi Publishing Corporation. 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.

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.