On Successive Approximations for Compact-Valued Nonexpansive Mappings
Set-valued and variational analysis(2023)
摘要
We show that for a given initial point the typical, in the sense of Baire category, nonexpansive compact valued mapping F has the following properties: there is a unique sequence of successive approximations and this sequence converges to a fixed point of F. In the case of separable Banach spaces we show that for the typical mapping there is a residual set of initial points that have a unique trajectory.
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关键词
Banach space,Generic property,Set-valued nonexpansive mapping,Successive approximations
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