On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces
Park, Sehie
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 263-268 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1996-01-01
Classification:  47H10,  54H25 
@article{118831,
     author = {Sehie Park},
     title = {On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {263-268},
     zbl = {0852.47029},
     mrnumber = {1399001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118831}
}

Park, Sehie. On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 263-268. http://gdmltest.u-ga.fr/item/118831/

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