Abstract
In this note the continuation principle (nonlinear alternative) for nonexpansive maps on Hilbert spaces (see [5]) in extended in two directions: 1) to the case of uniformly convex Banach spaces; 2) for nonexpansive maps on a not necessarly convex set of a Hilbert space. In the proofs we use the Leray-Schauder continuation principle for condensing maps [7] , [9] (we can also Granas’ continuation principle for contractions on complete metric spaces [6].
Authors
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
?
Paper coordinates
R. Precup, On the continuation principle for nonexpansive maps, Studia Univ. Babeş-Bolyai Math. 41 (1996) no. 3 , 85-89.
About this paper
Journal
Studia Universitatis Babes-Bolyai Mathematica
Publisher Name
Universitatis ”Babeș-Bolyai”
paper on journal website
Print ISSN
0252-1938
Online ISSN
2065-961X
MR: 1 644 466
google scholar link