Krzysztof Pupka
Fixed points of periodic and firmly lipschitzian mappings in Banach spaces

Abstract:W.A.~Kirk in 1971 showed that if $T\colon C\to C$, where $C$ is a closed and convex subset of a Banach space, is $n$-periodic and uniformly $k$-lipschitzian mapping with $k2$ in any Banach space. We also show that $\operatorname{Fix}(T)$ is a H\"older continuous retract of $C$.

Keywords: lipschitzian mapping, firmly lipschitzian mapping, $n$-periodic mapping, fixed point, retractions
AMS Subject Classification: 47H09 47H10