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arXiv · 2203.03470

On Successive Approximations for Compact-Valued Nonexpansive Mappings

Emir Medjic
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Abstract

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 unique trajectory.

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Emir Medjic. 2022-03-07. On Successive Approximations for Compact-Valued Nonexpansive Mappings. https://arxiv.org/abs/2203.03470

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