On the structure of fixed point sets of asymptotically regular mappings in Hilbert spaces
Keywords
Asymptotically regular mapping, retraction, asymptotic center, fixed point, Hilbert spaceAbstract
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 $C$.Downloads
Published
2009-12-01
How to Cite
1.
GÓRNICKI, Jarosław. On the structure of fixed point sets of asymptotically regular mappings in Hilbert spaces. Topological Methods in Nonlinear Analysis [online]. 1 December 2009, T. 34, nr 2, s. 383–389. [accessed 29.3.2023].
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