On the structure of fixed point sets of asymptotically regular mappings in Hilbert spaces
Słowa kluczowe
Asymptotically regular mapping, retraction, asymptotic center, fixed point, Hilbert spaceAbstrakt
The purpose of this paper is to prove the following theorem: Let $H$ be a Hilbert space, let $C$ be a nonempty bounded closed convex subset of $H$ and let $T\colon C\rightarrow C$ be an asymptotically regular mapping. If $$ \liminf_{n\rightarrow \infty} \|T^n\|< \sqrt{2}, $$ then $Fix T=\{x\in C:Tx=x\}$ is a retract of $C$.Pobrania
Opublikowane
2009-12-01
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1.
GÓRNICKI, Jarosław. On the structure of fixed point sets of asymptotically regular mappings in Hilbert spaces. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2009, T. 34, nr 2, s. 383–389. [udostępniono 22.7.2024].
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