Browder ’ s Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces

@inproceedings{Acedo2009BrowderS,
  title={Browder ’ s Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces},
  author={Genaro L{\'o}pez Acedo and Tomonari Suzuki},
  year={2009}
}
Let C be a closed convex subset of a Hilbert space E. A mapping T on C is called a nonexpansive mapping if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. We denote by F T the set of fixed points of T . Browder, see 1 , proved that F T is nonempty provided that C is, in addition, bounded. Kirk in a very celebrated paper, see 2 , extended this result to the setting of reflexive Banach spaces with normal structure. Browder 3 initiated the investigation of an implicit method for approximating fixed points… CONTINUE READING

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