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Keywords:
rotative mappings; fixed points
rotative mappings; fixed points
Summary:
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 $n=2,3$.
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