On generic convergence of successive approximations of mappings with convex and compact point images

We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of...

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Detalles Bibliográficos
Autores principales: Bargetz, Christian, Medjic, Emir, Pirk, Katriin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/
https://www.ncbi.nlm.nih.gov/pubmed/37846215
http://dx.doi.org/10.1007/s00605-022-01813-y
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author Bargetz, Christian
Medjic, Emir
Pirk, Katriin
author_facet Bargetz, Christian
Medjic, Emir
Pirk, Katriin
author_sort Bargetz, Christian
collection PubMed
description We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.
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spelling pubmed-105767362023-10-16 On generic convergence of successive approximations of mappings with convex and compact point images Bargetz, Christian Medjic, Emir Pirk, Katriin Mon Hefte Math Article We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping. Springer Vienna 2022-12-22 2023 /pmc/articles/PMC10576736/ /pubmed/37846215 http://dx.doi.org/10.1007/s00605-022-01813-y Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bargetz, Christian
Medjic, Emir
Pirk, Katriin
On generic convergence of successive approximations of mappings with convex and compact point images
title On generic convergence of successive approximations of mappings with convex and compact point images
title_full On generic convergence of successive approximations of mappings with convex and compact point images
title_fullStr On generic convergence of successive approximations of mappings with convex and compact point images
title_full_unstemmed On generic convergence of successive approximations of mappings with convex and compact point images
title_short On generic convergence of successive approximations of mappings with convex and compact point images
title_sort on generic convergence of successive approximations of mappings with convex and compact point images
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/
https://www.ncbi.nlm.nih.gov/pubmed/37846215
http://dx.doi.org/10.1007/s00605-022-01813-y
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