Krzysztof Pupka
Abstract
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summary: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 $k 2$ in any Banach space. We also show that $\operatorname{Fix}(T)$ is a Hölder continuous retract of $C$.
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summary: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 $k 2$ in any Banach space. We also show that $\operatorname{Fix}(T)$ is a Hölder continuous retract of $C$.
Key concepts: Retract, Banach space, Mathematics, Uniformly convex space, Pure mathematics, Regular polygon, Fixed point, Space (punctuation)