Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 495-510
  • ISSN: 0010-2628

Abstract

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Let C be a nonempty closed convex subset of a Banach space E and T : C → C a k -Lipschitzian rotative mapping, i.eṡuch that ∥ T x - T y ∥ ≤ k · ∥ x - y ∥ and ∥ T n x - x ∥ ≤ a · ∥ x - T x ∥ for some real k , a and an integer n > a . The paper concerns the existence of a fixed point of T in p -uniformly convex Banach spaces, depending on k , a and n = 2 , 3 .

How to cite

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Górnicki, Jarosław. "Remarks on fixed points of rotative Lipschitzian mappings." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 495-510. <http://eudml.org/doc/248390>.

@article{Górnicki1999,
abstract = {Let $C$ be a nonempty closed convex subset of a Banach space $E$ and $T:C\rightarrow C$ a $k$-Lipschitzian rotative mapping, i.eṡuch that $\Vert Tx-Ty\Vert \le k\cdot \Vert x-y\Vert $ and $\Vert T^n x-x\Vert \le a\cdot \Vert x-Tx\Vert $ for some real $k$, $a$ and an integer $n>a$. The paper concerns the existence of a fixed point of $T$ in $p$-uniformly convex Banach spaces, depending on $k$, $a$ and $n=2,3$.},
author = {Górnicki, Jarosław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {rotative mappings; fixed points; rotative mappings; fixed points; Banach spaces},
language = {eng},
number = {3},
pages = {495-510},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on fixed points of rotative Lipschitzian mappings},
url = {http://eudml.org/doc/248390},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Górnicki, Jarosław
TI - Remarks on fixed points of rotative Lipschitzian mappings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 495
EP - 510
AB - Let $C$ be a nonempty closed convex subset of a Banach space $E$ and $T:C\rightarrow C$ a $k$-Lipschitzian rotative mapping, i.eṡuch that $\Vert Tx-Ty\Vert \le k\cdot \Vert x-y\Vert $ and $\Vert T^n x-x\Vert \le a\cdot \Vert x-Tx\Vert $ for some real $k$, $a$ and an integer $n>a$. The paper concerns the existence of a fixed point of $T$ in $p$-uniformly convex Banach spaces, depending on $k$, $a$ and $n=2,3$.
LA - eng
KW - rotative mappings; fixed points; rotative mappings; fixed points; Banach spaces
UR - http://eudml.org/doc/248390
ER -

References

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