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Zbl 0947.47049
Takahashi, Wataru; Kim, Gang-Eun
Strong convergence of approximants to fixed points of nonexpansive nonself-mappings in Banach spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl. 32, No.3, 447-454 (1998). ISSN 0362-546X

Let $E$ be a reflexive Banach space with uniformly Gâteaux differentiable norm, $C$ a closed convex subset of $E$ and $T: C\to C$ be a nonexpansive mapping (or $T: C\to E$). In both cases the existence of fixed points is expressed in terms of strong convergence theorems.
[L.Górniewicz (Toruń)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: reflexive Banach space; uniformly Gâteaux differentiable norm; nonexpansive mapping; fixed points; strong convergence theorems

Cited in: Zbl 1138.47052 Zbl 1103.47047

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