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Zbl 0849.47030
Bruck, Ronald; Kuczumow, Tadeusz; Reich, Simeon
Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property.
(English)
[J] Colloq. Math. 65, No.2, 169-179 (1993). ISSN 0010-1354; ISSN 1730-6302/e

The authors study asymptotically nonexpensive mappings in the intermediate sense, $T: C\to C$, on a not necessarily convex subset $C$ of a Banach space with the Opial condition, $X$, i.e. $$\limsup_{n\to \infty} \sup_{x,y\in C} (|T^n x- T^n y|- |x-y |)\leq 0.$$ For such maps fixed points are constructed.
MSC 2000:
*47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: asymptotically nonexpensive mappings in the intermediate sense; Banach space with the Opial condition; fixed points

Cited in: Zbl 0880.47047

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