Fixed points of asymptotically regular mappings in spaces with uniformly normal structure
Górnicki, Jarosław
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 639-643 / Harvested from Czech Digital Mathematics Library
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It is proved that: for every Banach space $X$ which has uniformly normal structure there exists a $k>1$ with the property: if $A$ is a nonempty bounded closed convex subset of $X$ and $T:A\rightarrow A$ is an asymptotically regular mapping such that $$ \liminf _{n\rightarrow \infty } |\kern -0.8pt|\kern -0.8pt|T^n|\kern -0.8pt|\kern -0.8pt|< k, $$ where $|\kern -0.8pt|\kern -0.8pt|T|\kern -0.8pt|\kern -0.8pt|$ is the Lipschitz constant (norm) of $T$, then $T$ has a fixed point in $A$.

Publié le : 1991-01-01
Classification:  46B20,  47H10 
@article{118443,
     author = {Jaros\l aw G\'ornicki},
     title = {Fixed points of asymptotically regular mappings in spaces with uniformly normal structure},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {639-643},
     zbl = {0768.47027},
     mrnumber = {1159810},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118443}
}

Górnicki, Jarosław. Fixed points of asymptotically regular mappings in spaces with uniformly normal structure. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 639-643. http://gdmltest.u-ga.fr/item/118443/

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