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Title: On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces (English)
Author: Park, Sehie
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 37
Issue: 2
Year: 1996
Pages: 263-268
Category: math
Summary: Let $X$ be a uniformly convex Banach space, $D\subset X$, $f:D\to X$ a nonexpansive map, and $K$ a closed bounded subset such that $\overline{\text{co}}\,K\subset D$. If (1) $f|_K$ is weakly inward and $K$ is star-shaped or (2) $f|_K$ satisfies the Leray-Schauder boundary condition, then $f$ has a fixed point in $\overline{\text{co}}\,K$. This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others. (English)
Keyword: uniformly convex
Keyword: Banach space
Keyword: Hilbert space
Keyword: contraction
Keyword: nonexpansive map
Keyword: weakly inward map
Keyword: demi-closed
Keyword: Rothe condition
Keyword: Leray-Schauder condition
Keyword: (KR)-bounded
Keyword: Opial's condition
MSC: 47H10
MSC: 54H25
idZBL: Zbl 0852.47029
idMR: MR1399001
Date available: 2009-01-08T18:23:31Z
Last updated: 2012-04-30
Stable URL:
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