An Iteration Method for Nonexpansive Mappings in Hilbert Spaces
<p/> <p>In real Hilbert space <inline-formula><graphic file="1687-1812-2007-028619-i1.gif"/></inline-formula>, from an arbitrary initial point <inline-formula><graphic file="1687-1812-2007-028619-i2.gif"/></inline-formula>, an expli...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2007-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2007/028619 |
| _version_ | 1818998803814940672 |
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| author | Wang Lin |
| author_facet | Wang Lin |
| author_sort | Wang Lin |
| collection | DOAJ |
| description | <p/> <p>In real Hilbert space <inline-formula><graphic file="1687-1812-2007-028619-i1.gif"/></inline-formula>, from an arbitrary initial point <inline-formula><graphic file="1687-1812-2007-028619-i2.gif"/></inline-formula>, an explicit iteration scheme is defined as follows: <inline-formula><graphic file="1687-1812-2007-028619-i3.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1812-2007-028619-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2007-028619-i5.gif"/></inline-formula> is a nonexpansive mapping such that <inline-formula><graphic file="1687-1812-2007-028619-i6.gif"/></inline-formula> is nonempty, <inline-formula><graphic file="1687-1812-2007-028619-i7.gif"/></inline-formula> is a <inline-formula><graphic file="1687-1812-2007-028619-i8.gif"/></inline-formula>-strongly monotone and <inline-formula><graphic file="1687-1812-2007-028619-i9.gif"/></inline-formula>-Lipschitzian mapping, <inline-formula><graphic file="1687-1812-2007-028619-i10.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1812-2007-028619-i11.gif"/></inline-formula>. Under some suitable conditions, the sequence <inline-formula><graphic file="1687-1812-2007-028619-i12.gif"/></inline-formula> is shown to converge strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i13.gif"/></inline-formula> and the necessary and sufficient conditions that <inline-formula><graphic file="1687-1812-2007-028619-i14.gif"/></inline-formula> converges strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i15.gif"/></inline-formula> are obtained.</p> |
| first_indexed | 2024-12-20T22:07:20Z |
| format | Article |
| id | doaj.art-38aeafcbfe9f4fe3b5975122c28d6764 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T22:07:20Z |
| publishDate | 2007-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-38aeafcbfe9f4fe3b5975122c28d67642022-12-21T19:25:14ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122007-01-0120071028619An Iteration Method for Nonexpansive Mappings in Hilbert SpacesWang Lin<p/> <p>In real Hilbert space <inline-formula><graphic file="1687-1812-2007-028619-i1.gif"/></inline-formula>, from an arbitrary initial point <inline-formula><graphic file="1687-1812-2007-028619-i2.gif"/></inline-formula>, an explicit iteration scheme is defined as follows: <inline-formula><graphic file="1687-1812-2007-028619-i3.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1812-2007-028619-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2007-028619-i5.gif"/></inline-formula> is a nonexpansive mapping such that <inline-formula><graphic file="1687-1812-2007-028619-i6.gif"/></inline-formula> is nonempty, <inline-formula><graphic file="1687-1812-2007-028619-i7.gif"/></inline-formula> is a <inline-formula><graphic file="1687-1812-2007-028619-i8.gif"/></inline-formula>-strongly monotone and <inline-formula><graphic file="1687-1812-2007-028619-i9.gif"/></inline-formula>-Lipschitzian mapping, <inline-formula><graphic file="1687-1812-2007-028619-i10.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1812-2007-028619-i11.gif"/></inline-formula>. Under some suitable conditions, the sequence <inline-formula><graphic file="1687-1812-2007-028619-i12.gif"/></inline-formula> is shown to converge strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i13.gif"/></inline-formula> and the necessary and sufficient conditions that <inline-formula><graphic file="1687-1812-2007-028619-i14.gif"/></inline-formula> converges strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i15.gif"/></inline-formula> are obtained.</p>http://www.fixedpointtheoryandapplications.com/content/2007/028619 |
| spellingShingle | Wang Lin An Iteration Method for Nonexpansive Mappings in Hilbert Spaces Fixed Point Theory and Applications |
| title | An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
| title_full | An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
| title_fullStr | An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
| title_full_unstemmed | An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
| title_short | An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
| title_sort | iteration method for nonexpansive mappings in hilbert spaces |
| url | http://www.fixedpointtheoryandapplications.com/content/2007/028619 |
| work_keys_str_mv | AT wanglin aniterationmethodfornonexpansivemappingsinhilbertspaces AT wanglin iterationmethodfornonexpansivemappingsinhilbertspaces |