On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text] . Then, for a fixed [Formula: see text] and for [Formula: see text] , Krasnoselskii–Mann algorithm is defined b...

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Detalles Bibliográficos
Autores principales: Guo, Meifang, Li, Xia, Su, Yongfu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4980868/
https://www.ncbi.nlm.nih.gov/pubmed/27563523
http://dx.doi.org/10.1186/s40064-016-2977-8
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author Guo, Meifang
Li, Xia
Su, Yongfu
author_facet Guo, Meifang
Li, Xia
Su, Yongfu
author_sort Guo, Meifang
collection PubMed
description Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text] . Then, for a fixed [Formula: see text] and for [Formula: see text] , Krasnoselskii–Mann algorithm is defined by [Formula: see text] where [Formula: see text] . Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them.
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spelling pubmed-49808682016-08-25 On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings” Guo, Meifang Li, Xia Su, Yongfu Springerplus Research Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text] . Then, for a fixed [Formula: see text] and for [Formula: see text] , Krasnoselskii–Mann algorithm is defined by [Formula: see text] where [Formula: see text] . Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them. Springer International Publishing 2016-08-11 /pmc/articles/PMC4980868/ /pubmed/27563523 http://dx.doi.org/10.1186/s40064-016-2977-8 Text en © The Author(s) 2016 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
Guo, Meifang
Li, Xia
Su, Yongfu
On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title_full On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title_fullStr On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title_full_unstemmed On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title_short On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”
title_sort on an open question of v. colao and g. marino presented in the paper “krasnoselskii–mann method for non-self mappings”
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4980868/
https://www.ncbi.nlm.nih.gov/pubmed/27563523
http://dx.doi.org/10.1186/s40064-016-2977-8
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