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.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 $n=2,3$.
Keywords: rotative mappings, fixed points
AMS Subject Classification: 47H09, 47H10