Abstract
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 ${\rm Fix}\, T=\{x\in C:Tx=x\}$ is a retract of $C$.
Citation
Jarosław Górnicki. "On the structure of fixed point sets of asymptotically regular mappings in Hilbert spaces." Topol. Methods Nonlinear Anal. 34 (2) 383 - 389, 2009.
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