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

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

Keywords

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Paper coordinates

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

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About this paper

Journal

Studia Universitatis Babes-Bolyai Mathematica

Publisher Name

Universitatis ”Babeș-Bolyai”

Print ISSN

0252-1938

Online ISSN

2065-961X

MR: 1 644 466

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[6] granas, A., Continuation method for contractive maps, Topol. Methods Nonlinear Anal., 3, 375-379, 1994.
[7] Krawcewicz, W., Contribution a la theorie des equations non lineaires dans les espaces de Banach, Dissertationes Math. 273, 198…
[8] Pavel, N., Ecuații diferențiale asociate unor operatori neliniari pe spații Banach, Ed. Acad. R.S.R., București, 1977.
[9] Precup, R., Nonlinear boundary value problems for infinite systems of second-order functional differential equations, Seminar on Differential Equaitons (Editor I.A.Rus), pp. 17-30, University Babes-Bolyai, Cluj, 1988

1996

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