Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators
<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-81325-i2.gif"/></inline-formula> be a real reflexive Banach space, let <inline-formula><graphic file="1687-1812-2006-81325-i3.gif"/></inline-formula> be a closed convex subse...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2006-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2006/81325 |
| _version_ | 1819000658451234816 |
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| author | Chen Rudong Zhu Zhichuan |
| author_facet | Chen Rudong Zhu Zhichuan |
| author_sort | Chen Rudong |
| collection | DOAJ |
| description | <p/> <p>Let <inline-formula><graphic file="1687-1812-2006-81325-i2.gif"/></inline-formula> be a real reflexive Banach space, let <inline-formula><graphic file="1687-1812-2006-81325-i3.gif"/></inline-formula> be a closed convex subset of <inline-formula><graphic file="1687-1812-2006-81325-i4.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i5.gif"/></inline-formula> be an <inline-formula><graphic file="1687-1812-2006-81325-i6.gif"/></inline-formula>-accretive operator with a zero. Consider the iterative method that generates the sequence <inline-formula><graphic file="1687-1812-2006-81325-i7.gif"/></inline-formula> by the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i8.gif"/></inline-formula> where <inline-formula><graphic file="1687-1812-2006-81325-i9.gif"/></inline-formula> and <inline-formula><graphic file="1687-1812-2006-81325-i10.gif"/></inline-formula> are two sequences satisfying certain conditions, <inline-formula><graphic file="1687-1812-2006-81325-i11.gif"/></inline-formula> denotes the resolvent <inline-formula><graphic file="1687-1812-2006-81325-i12.gif"/></inline-formula> for <inline-formula><graphic file="1687-1812-2006-81325-i13.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i14.gif"/></inline-formula> be a fixed contractive mapping. The strong convergence of the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i15.gif"/></inline-formula> is proved assuming that <inline-formula><graphic file="1687-1812-2006-81325-i16.gif"/></inline-formula> has a weakly continuous duality map.</p> |
| first_indexed | 2024-12-20T22:36:49Z |
| format | Article |
| id | doaj.art-3806dbf9fbf040849ffe21d31f887ff8 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T22:36:49Z |
| publishDate | 2006-01-01 |
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| series | Fixed Point Theory and Applications |
| spelling | doaj.art-3806dbf9fbf040849ffe21d31f887ff82022-12-21T19:24:35ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-01-012006181325Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operatorsChen RudongZhu Zhichuan<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-81325-i2.gif"/></inline-formula> be a real reflexive Banach space, let <inline-formula><graphic file="1687-1812-2006-81325-i3.gif"/></inline-formula> be a closed convex subset of <inline-formula><graphic file="1687-1812-2006-81325-i4.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i5.gif"/></inline-formula> be an <inline-formula><graphic file="1687-1812-2006-81325-i6.gif"/></inline-formula>-accretive operator with a zero. Consider the iterative method that generates the sequence <inline-formula><graphic file="1687-1812-2006-81325-i7.gif"/></inline-formula> by the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i8.gif"/></inline-formula> where <inline-formula><graphic file="1687-1812-2006-81325-i9.gif"/></inline-formula> and <inline-formula><graphic file="1687-1812-2006-81325-i10.gif"/></inline-formula> are two sequences satisfying certain conditions, <inline-formula><graphic file="1687-1812-2006-81325-i11.gif"/></inline-formula> denotes the resolvent <inline-formula><graphic file="1687-1812-2006-81325-i12.gif"/></inline-formula> for <inline-formula><graphic file="1687-1812-2006-81325-i13.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i14.gif"/></inline-formula> be a fixed contractive mapping. The strong convergence of the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i15.gif"/></inline-formula> is proved assuming that <inline-formula><graphic file="1687-1812-2006-81325-i16.gif"/></inline-formula> has a weakly continuous duality map.</p>http://www.fixedpointtheoryandapplications.com/content/2006/81325 |
| spellingShingle | Chen Rudong Zhu Zhichuan Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators Fixed Point Theory and Applications |
| title | Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators |
| title_full | Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators |
| title_fullStr | Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators |
| title_full_unstemmed | Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators |
| title_short | Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators |
| title_sort | viscosity approximation fixed points for nonexpansive and inline formula graphic file 1687 1812 2006 81325 i1 gif inline formula accretive operators |
| url | http://www.fixedpointtheoryandapplications.com/content/2006/81325 |
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