Loading…
Strong convergence theorems by the hybrid method for families of mappings in Banach spaces
Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is Gâteaux differentiable and let { T n } be a family of mappings of C into itself such that the set of all common fixed points of { T n } is nonempty. We consider a sequence { x n } generated by the hybrid meth...
Saved in:
| Published in: | Nonlinear analysis 2009-08, Vol.71 (3), p.812-818 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3 |
| container_end_page | 818 |
| container_issue | 3 |
| container_start_page | 812 |
| container_title | Nonlinear analysis |
| container_volume | 71 |
| creator | Nakajo, Kazuhide Shimoji, Kazuya Takahashi, Wataru |
| description | Let
C
be a nonempty closed convex subset of a uniformly convex Banach space
E
whose norm is Gâteaux differentiable and let
{
T
n
}
be a family of mappings of
C
into itself such that the set of all common fixed points of
{
T
n
}
is nonempty. We consider a sequence
{
x
n
}
generated by the hybrid method in mathematical programming. And we give the conditions of
{
T
n
}
under which
{
x
n
}
converges strongly to a common fixed point of
{
T
n
}
and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445]. |
| doi_str_mv | 10.1016/j.na.2008.10.108 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_34532030</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X08006937</els_id><sourcerecordid>34532030</sourcerecordid><originalsourceid>FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3</originalsourceid><addsrcrecordid>eNp1UE1vEzEQtRBIhJY7R1_gtmH8sd4tN6hoQarEoSAhLtZkMk4c7dqLva2Uf8-GVNw4zejpvTdvnhBvFKwVKPf-sE641gD9-i_SPxMr1XemabVqn4sVGKeb1rqfL8WrWg8AoDrjVuLX_Vxy2knK6ZHLjhOxnPecC49Vbo6nXe6PmxK3cuR5n7cy5CIDjnGIXGUOcsRpimlXZUzyEyakvawTEtdL8SLgUPn107wQP24-f7_-0tx9u_16_fGuIavV3PQdYK_cVQ-0AQsdKHLA7Di4jtmqQLzkps7qFi1ZcqFzV7ozBo2FNqC5EO_OvlPJvx-4zn6MlXgYMHF-qN7Y1mgwsBDhTKSSay0c_FTiiOXoFfhTif7gE_pTiWekXyRvn7yxEg6hYKJY_-m0skt80Avvw5nHy6OPkYuvFE9lbmNhmv02x_8f-QNIJIXx</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>34532030</pqid></control><display><type>article</type><title>Strong convergence theorems by the hybrid method for families of mappings in Banach spaces</title><source>ScienceDirect Freedom Collection</source><source>Backfile Package - Mathematics</source><creator>Nakajo, Kazuhide ; Shimoji, Kazuya ; Takahashi, Wataru</creator><creatorcontrib>Nakajo, Kazuhide ; Shimoji, Kazuya ; Takahashi, Wataru</creatorcontrib><description>Let
C
be a nonempty closed convex subset of a uniformly convex Banach space
E
whose norm is Gâteaux differentiable and let
{
T
n
}
be a family of mappings of
C
into itself such that the set of all common fixed points of
{
T
n
}
is nonempty. We consider a sequence
{
x
n
}
generated by the hybrid method in mathematical programming. And we give the conditions of
{
T
n
}
under which
{
x
n
}
converges strongly to a common fixed point of
{
T
n
}
and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445].</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2008.10.108</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Convex feasibility problem ; Exact sciences and technology ; Functional analysis ; Hybrid method ; Mathematical analysis ; Mathematics ; Monotone operator ; Proximal point algorithm ; Sciences and techniques of general use ; Strong convergence</subject><ispartof>Nonlinear analysis, 2009-08, Vol.71 (3), p.812-818</ispartof><rights>2008 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3</citedby><cites>FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X08006937$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3564,27924,27925,46003</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21487002$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Nakajo, Kazuhide</creatorcontrib><creatorcontrib>Shimoji, Kazuya</creatorcontrib><creatorcontrib>Takahashi, Wataru</creatorcontrib><title>Strong convergence theorems by the hybrid method for families of mappings in Banach spaces</title><title>Nonlinear analysis</title><description>Let
C
be a nonempty closed convex subset of a uniformly convex Banach space
E
whose norm is Gâteaux differentiable and let
{
T
n
}
be a family of mappings of
C
into itself such that the set of all common fixed points of
{
T
n
}
is nonempty. We consider a sequence
{
x
n
}
generated by the hybrid method in mathematical programming. And we give the conditions of
{
T
n
}
under which
{
x
n
}
converges strongly to a common fixed point of
{
T
n
}
and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445].</description><subject>Convex feasibility problem</subject><subject>Exact sciences and technology</subject><subject>Functional analysis</subject><subject>Hybrid method</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Monotone operator</subject><subject>Proximal point algorithm</subject><subject>Sciences and techniques of general use</subject><subject>Strong convergence</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1UE1vEzEQtRBIhJY7R1_gtmH8sd4tN6hoQarEoSAhLtZkMk4c7dqLva2Uf8-GVNw4zejpvTdvnhBvFKwVKPf-sE641gD9-i_SPxMr1XemabVqn4sVGKeb1rqfL8WrWg8AoDrjVuLX_Vxy2knK6ZHLjhOxnPecC49Vbo6nXe6PmxK3cuR5n7cy5CIDjnGIXGUOcsRpimlXZUzyEyakvawTEtdL8SLgUPn107wQP24-f7_-0tx9u_16_fGuIavV3PQdYK_cVQ-0AQsdKHLA7Di4jtmqQLzkps7qFi1ZcqFzV7ozBo2FNqC5EO_OvlPJvx-4zn6MlXgYMHF-qN7Y1mgwsBDhTKSSay0c_FTiiOXoFfhTif7gE_pTiWekXyRvn7yxEg6hYKJY_-m0skt80Avvw5nHy6OPkYuvFE9lbmNhmv02x_8f-QNIJIXx</recordid><startdate>20090801</startdate><enddate>20090801</enddate><creator>Nakajo, Kazuhide</creator><creator>Shimoji, Kazuya</creator><creator>Takahashi, Wataru</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20090801</creationdate><title>Strong convergence theorems by the hybrid method for families of mappings in Banach spaces</title><author>Nakajo, Kazuhide ; Shimoji, Kazuya ; Takahashi, Wataru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Convex feasibility problem</topic><topic>Exact sciences and technology</topic><topic>Functional analysis</topic><topic>Hybrid method</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Monotone operator</topic><topic>Proximal point algorithm</topic><topic>Sciences and techniques of general use</topic><topic>Strong convergence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nakajo, Kazuhide</creatorcontrib><creatorcontrib>Shimoji, Kazuya</creatorcontrib><creatorcontrib>Takahashi, Wataru</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nakajo, Kazuhide</au><au>Shimoji, Kazuya</au><au>Takahashi, Wataru</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strong convergence theorems by the hybrid method for families of mappings in Banach spaces</atitle><jtitle>Nonlinear analysis</jtitle><date>2009-08-01</date><risdate>2009</risdate><volume>71</volume><issue>3</issue><spage>812</spage><epage>818</epage><pages>812-818</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>Let
C
be a nonempty closed convex subset of a uniformly convex Banach space
E
whose norm is Gâteaux differentiable and let
{
T
n
}
be a family of mappings of
C
into itself such that the set of all common fixed points of
{
T
n
}
is nonempty. We consider a sequence
{
x
n
}
generated by the hybrid method in mathematical programming. And we give the conditions of
{
T
n
}
under which
{
x
n
}
converges strongly to a common fixed point of
{
T
n
}
and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445].</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2008.10.108</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2009-08, Vol.71 (3), p.812-818 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_34532030 |
| source | ScienceDirect Freedom Collection; Backfile Package - Mathematics |
| subjects | Convex feasibility problem Exact sciences and technology Functional analysis Hybrid method Mathematical analysis Mathematics Monotone operator Proximal point algorithm Sciences and techniques of general use Strong convergence |
| title | Strong convergence theorems by the hybrid method for families of mappings in Banach spaces |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T22%3A50%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Strong%20convergence%20theorems%20by%20the%20hybrid%20method%20for%20families%20of%20mappings%20in%20Banach%20spaces&rft.jtitle=Nonlinear%20analysis&rft.au=Nakajo,%20Kazuhide&rft.date=2009-08-01&rft.volume=71&rft.issue=3&rft.spage=812&rft.epage=818&rft.pages=812-818&rft.issn=0362-546X&rft.eissn=1873-5215&rft.coden=NOANDD&rft_id=info:doi/10.1016/j.na.2008.10.108&rft_dat=%3Cproquest_cross%3E34532030%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c421t-870a816980cb040701c60ee6ef67ee41fce546c7425a4c4c6f7692733a3405fa3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=34532030&rft_id=info:pmid/&rfr_iscdi=true |