Geodesic
Remarks on fixed points of rotative Lipschitzian mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 495-510.

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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 $n=2,3$.
Classification : 47H09, 47H10
Keywords: rotative mappings; fixed points 
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     author = {G\'ornicki, Jaros{\l}aw},
     title = {Remarks on fixed points of rotative {Lipschitzian} mappings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {495--510},
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     zbl = {1065.47504},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a9/}
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Górnicki, Jarosław. Remarks on fixed points of rotative Lipschitzian mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 495-510. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a9/