### Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let $C$ be a nonempty closed convex subset of a Banach space $E$ and $T:C\to C$ a $k$-Lipschitzian rotative mapping, i.eṡuch that $\parallel Tx-Ty\parallel \le k\xb7\parallel x-y\parallel $ and $\parallel {T}^{n}x-x\parallel \le a\xb7\parallel x-Tx\parallel $ 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 $n=2,3$.