On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature

Bargetz, Christian; Dymond, Michael; Medjic, Emir; Reich, Simeon

doi:10.12775/tmna.2020.040

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Cited by 2 publications

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“…The problems discussed above have also been studied in more general metric spaces and for more general classes of mappings; see, for example, [11], [3] and [2].…”

Section: Introductionmentioning

confidence: 99%

Porosity phenomena of non-expansive, Banach space mappings

Dymond¹

2021

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For any non-trivial convex and bounded subset C of a Banach space, we show that outside of a σ-porous subset of the space of non-expansive mappings C → C, all mappings have the maximal Lipschitz constant one witnessed locally at typical points of C. This extends a result of Bargetz and the author from separable Banach spaces to all Banach spaces and the proof given is completely independent. We further establish a fine relationship between the classes of exceptional sets involved in this statement, captured by the hierarchy of notions of φ-porosity.

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“…The problems discussed above have also been studied in more general metric spaces and for more general classes of mappings; see, for example, [11], [3] and [2].…”

Section: Introductionmentioning

confidence: 99%