# On the continuation principle for nonexpansive maps

## 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

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

?

## Paper coordinates

R. Precup, On the continuation principle for nonexpansive maps, Studia Univ. Babeş-Bolyai Math. 41 (1996) no. 3 , 85-89.

## PDF

##### Journal

Studia Universitatis Babes-Bolyai Mathematica

##### Publisher Name

Universitatis ”Babeș-Bolyai”

0252-1938

2065-961X

MR: 1 644 466