A nonlinear ergodic theorem for a reversible semigroup of nonexpansive mappings in a Hilbert space
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- by Wataru Takahashi PDF
- Proc. Amer. Math. Soc. 97 (1986), 55-58 Request permission
Abstract:
Let $C$ be a nonempty closed convex subset of a Hilbert space, $S$ a right reversible semitopological semigroup, $\mathcal {S} = \{ {T_t}:t \in S\}$ a continuous representation of $S$ as nonexpansive mappings on a closed convex subset $C$ into $C$, and $F(\mathcal {S})$ the set of common fixed points of mappings ${T_t},\;t \in S$. Then we deal with the existence of a nonexpansive retraction $P$ of $C$ onto $F(\mathcal {S})$ such that $P{T_t} = {T_t}P = P$ for each $t \in S$ and ${P_x}$ is contained in the closure of the convex hull of $\{ {T_t}x:t \in S\}$ for each $x \in C$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 55-58
- MSC: Primary 47H10; Secondary 47A35
- DOI: https://doi.org/10.1090/S0002-9939-1986-0831386-4
- MathSciNet review: 831386