A common fixed-point theorem in reflexive locally uniformly convex Banach spaces

A common fixed-point theorem in reflexive locally uniformly convex Banach spaces

Edelstein, Michael; Kiang, Mo Tak
Date:   1985-07
Type:   Text
ISSN:  0002-9939

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Proceedings of the American Mathematical Society 94(3), 411-415. (1985)

Abstract:

Let X be a reflexive locally uniformly convex Banach space and G an ultimately nonexpansive commutative semigroup of continuous self-maps of X. If there exists a point x in X recurrent under G such that G(x) is bounded, then G has a common fixed point in co(G(x)). If X is a Hubert space then there is exactly one such point in co(G(x)).

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Subject:
    Banach spaces

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Article is made available in accordance with the publisher’s policy and is subject to copyright law. Please refer to the publisher’s site. Any re-use of this article is to be in accordance with the publisher’s copyright policy. This posting is in no way granting any permission for re-use to the reader/user. First published in Proceedings of the American Mathematical Society in v.94, no.3, 1985, published by the American Mathematical Society.
 
 

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