Constructive techniques for zeros of monotone mappings in certain Banach spaces

Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the a...

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Detalles Bibliográficos
Autores principales: Diop, C, Sow, T M M, Djitte, N, Chidume, C E
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2015
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4516154/
https://www.ncbi.nlm.nih.gov/pubmed/26240781
http://dx.doi.org/10.1186/s40064-015-1169-2
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author Diop, C
Sow, T M M
Djitte, N
Chidume, C E
author_facet Diop, C
Sow, T M M
Djitte, N
Chidume, C E
author_sort Diop, C
collection PubMed
description Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text] where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem.
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spelling pubmed-45161542015-08-03 Constructive techniques for zeros of monotone mappings in certain Banach spaces Diop, C Sow, T M M Djitte, N Chidume, C E Springerplus Research Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text] where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem. Springer International Publishing 2015-07-28 /pmc/articles/PMC4516154/ /pubmed/26240781 http://dx.doi.org/10.1186/s40064-015-1169-2 Text en © Diop et al. 2015 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Diop, C
Sow, T M M
Djitte, N
Chidume, C E
Constructive techniques for zeros of monotone mappings in certain Banach spaces
title Constructive techniques for zeros of monotone mappings in certain Banach spaces
title_full Constructive techniques for zeros of monotone mappings in certain Banach spaces
title_fullStr Constructive techniques for zeros of monotone mappings in certain Banach spaces
title_full_unstemmed Constructive techniques for zeros of monotone mappings in certain Banach spaces
title_short Constructive techniques for zeros of monotone mappings in certain Banach spaces
title_sort constructive techniques for zeros of monotone mappings in certain banach spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4516154/
https://www.ncbi.nlm.nih.gov/pubmed/26240781
http://dx.doi.org/10.1186/s40064-015-1169-2
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AT sowtmm constructivetechniquesforzerosofmonotonemappingsincertainbanachspaces
AT djitten constructivetechniquesforzerosofmonotonemappingsincertainbanachspaces
AT chidumece constructivetechniquesforzerosofmonotonemappingsincertainbanachspaces

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