Let $C$ be a nonempty closed convex subset of a Banach space $E$ and \linebreak $T:C\rightarrow C$ a $k$-Lipschitzian rotative mapping, i.e\. such that $\|Tx-Ty\|\leq k\cdot \|x-y\|$ and $\|T^n x-x\|\leq a\cdot \|x-Tx\|$ 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 $n=2,3$.
@article{119106,
author = {Jaros\l aw G\'ornicki},
title = {Remarks on fixed points of rotative Lipschitzian mappings},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {495-510},
zbl = {1065.47504},
mrnumber = {1732485},
language = {en},
url = {http://dml.mathdoc.fr/item/119106}
}
Górnicki, Jarosław. Remarks on fixed points of rotative Lipschitzian mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 495-510. http://gdmltest.u-ga.fr/item/119106/
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