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 a unique trajectory.
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Acknowledgements
This research was funded by the Austrian Science Fund (FWF): P 32523. I wish to thank Christian Bargetz for a lot of fruitful discussions, for reading this article carefully and his helpful comments. Furthermore I want to give special thanks to the referee for carefully reading this paper, pointing out mistakes and improvements and making valuable suggestions.
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Communicated by Claudia Sagastizabal.
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Medjic, E. On Successive Approximations for Compact-Valued Nonexpansive Mappings. Set-Valued Var. Anal 31, 24 (2023). https://doi.org/10.1007/s11228-023-00684-1
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DOI: https://doi.org/10.1007/s11228-023-00684-1