Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces
The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar B...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/272867 |
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| author | Eskandar Naraghirad Ngai-Ching Wong Jen-Chih Yao |
| author_facet | Eskandar Naraghirad Ngai-Ching Wong Jen-Chih Yao |
| author_sort | Eskandar Naraghirad |
| collection | DOAJ |
| description | The Opial property of Hilbert spaces and some other special Banach spaces
is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally,
nonspreading mappings. Unfortunately, not every Banach space shares the Opial property.
However, every Banach space has a similar Bregman-Opial property for Bregman distances.
In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading
mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish
weak and strong convergence theorems for Bregman nonspreading mappings. |
| format | Article |
| id | doaj-art-3da31a7d1ab940b39fbec099b2a1a0cd |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3da31a7d1ab940b39fbec099b2a1a0cd2025-08-20T02:07:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/272867272867Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach SpacesEskandar Naraghirad0Ngai-Ching Wong1Jen-Chih Yao2Department of Mathematics, Yasouj University, Yasouj 75918, IranDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, TaiwanCenter for General Education, Kaohsiung Medical University, Kaohsiung 807, TaiwanThe Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.http://dx.doi.org/10.1155/2014/272867 |
| spellingShingle | Eskandar Naraghirad Ngai-Ching Wong Jen-Chih Yao Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces |
| title_full | Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces |
| title_fullStr | Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces |
| title_full_unstemmed | Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces |
| title_short | Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces |
| title_sort | applications of bregman opial property to bregman nonspreading mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2014/272867 |
| work_keys_str_mv | AT eskandarnaraghirad applicationsofbregmanopialpropertytobregmannonspreadingmappingsinbanachspaces AT ngaichingwong applicationsofbregmanopialpropertytobregmannonspreadingmappingsinbanachspaces AT jenchihyao applicationsofbregmanopialpropertytobregmannonspreadingmappingsinbanachspaces |