Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

Jarosław Górnicki

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 639-643
  • ISSN: 0010-2628

Abstract

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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 → A is an asymptotically regular mapping such that lim inf n → ∞ | | | T n | | | < k , where | | | T | | | is the Lipschitz constant (norm) of T , then T has a fixed point in A .

How to cite

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Górnicki, Jarosław. "Fixed points of asymptotically regular mappings in spaces with uniformly normal structure." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 639-643. <http://eudml.org/doc/247296>.

@article{Górnicki1991,
abstract = {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 \[ \liminf \_\{n\rightarrow \infty \} |\hspace\{-0.8pt\}|\hspace\{-0.8pt\}|T^n|\hspace\{-0.8pt\}|\hspace\{-0.8pt\}|< k, \] where $|\hspace\{-0.8pt\}|\hspace\{-0.8pt\}|T|\hspace\{-0.8pt\}|\hspace\{-0.8pt\}|$ is the Lipschitz constant (norm) of $T$, then $T$ has a fixed point in $A$.},
author = {Górnicki, Jarosław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymptotically regular mappings; uniformly normal structure; fixed points; uniformly normal structure; asymptotically regular mapping; Lipschitz constant; fixed point},
language = {eng},
number = {4},
pages = {639-643},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fixed points of asymptotically regular mappings in spaces with uniformly normal structure},
url = {http://eudml.org/doc/247296},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Górnicki, Jarosław
TI - Fixed points of asymptotically regular mappings in spaces with uniformly normal structure
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 639
EP - 643
AB - 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 \[ \liminf _{n\rightarrow \infty } |\hspace{-0.8pt}|\hspace{-0.8pt}|T^n|\hspace{-0.8pt}|\hspace{-0.8pt}|< k, \] where $|\hspace{-0.8pt}|\hspace{-0.8pt}|T|\hspace{-0.8pt}|\hspace{-0.8pt}|$ is the Lipschitz constant (norm) of $T$, then $T$ has a fixed point in $A$.
LA - eng
KW - asymptotically regular mappings; uniformly normal structure; fixed points; uniformly normal structure; asymptotically regular mapping; Lipschitz constant; fixed point
UR - http://eudml.org/doc/247296
ER -

References

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