Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type
<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2008-672301-i1.gif"/></inline-formula> be a real <inline-formula> <graphic file="1687-1812-2008-672301-i2.gif"/></inline-formula>-uniformly smooth Banach space w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2008/672301 |
| _version_ | 1819006242140454912 |
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| author | Zhang Ying Guo Yan |
| author_facet | Zhang Ying Guo Yan |
| author_sort | Zhang Ying |
| collection | DOAJ |
| description | <p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2008-672301-i1.gif"/></inline-formula> be a real <inline-formula> <graphic file="1687-1812-2008-672301-i2.gif"/></inline-formula>-uniformly smooth Banach space which is also uniformly convex (e.g., <inline-formula> <graphic file="1687-1812-2008-672301-i3.gif"/></inline-formula> or <inline-formula> <graphic file="1687-1812-2008-672301-i4.gif"/></inline-formula> spaces <inline-formula> <graphic file="1687-1812-2008-672301-i5.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-1812-2008-672301-i6.gif"/></inline-formula> a nonempty closed convex subset of <inline-formula> <graphic file="1687-1812-2008-672301-i7.gif"/></inline-formula>. By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a <inline-formula> <graphic file="1687-1812-2008-672301-i8.gif"/></inline-formula>-strictly pseudocontractive mapping of Browder-Petryshyn type on <inline-formula> <graphic file="1687-1812-2008-672301-i9.gif"/></inline-formula> in condition thet the control sequence <inline-formula> <graphic file="1687-1812-2008-672301-i10.gif"/></inline-formula> is chosen so that (i) <inline-formula> <graphic file="1687-1812-2008-672301-i11.gif"/></inline-formula> (ii) <inline-formula> <graphic file="1687-1812-2008-672301-i12.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-1812-2008-672301-i13.gif"/></inline-formula>. Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.</p> |
| first_indexed | 2024-12-21T00:05:34Z |
| format | Article |
| id | doaj.art-f8bfdc45db4546529c5a82b0c7de6eb7 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-21T00:05:34Z |
| publishDate | 2008-01-01 |
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| series | Fixed Point Theory and Applications |
| spelling | doaj.art-f8bfdc45db4546529c5a82b0c7de6eb72022-12-21T19:22:29ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122008-01-0120081672301Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn TypeZhang YingGuo Yan<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2008-672301-i1.gif"/></inline-formula> be a real <inline-formula> <graphic file="1687-1812-2008-672301-i2.gif"/></inline-formula>-uniformly smooth Banach space which is also uniformly convex (e.g., <inline-formula> <graphic file="1687-1812-2008-672301-i3.gif"/></inline-formula> or <inline-formula> <graphic file="1687-1812-2008-672301-i4.gif"/></inline-formula> spaces <inline-formula> <graphic file="1687-1812-2008-672301-i5.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-1812-2008-672301-i6.gif"/></inline-formula> a nonempty closed convex subset of <inline-formula> <graphic file="1687-1812-2008-672301-i7.gif"/></inline-formula>. By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a <inline-formula> <graphic file="1687-1812-2008-672301-i8.gif"/></inline-formula>-strictly pseudocontractive mapping of Browder-Petryshyn type on <inline-formula> <graphic file="1687-1812-2008-672301-i9.gif"/></inline-formula> in condition thet the control sequence <inline-formula> <graphic file="1687-1812-2008-672301-i10.gif"/></inline-formula> is chosen so that (i) <inline-formula> <graphic file="1687-1812-2008-672301-i11.gif"/></inline-formula> (ii) <inline-formula> <graphic file="1687-1812-2008-672301-i12.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-1812-2008-672301-i13.gif"/></inline-formula>. Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.</p>http://www.fixedpointtheoryandapplications.com/content/2008/672301 |
| spellingShingle | Zhang Ying Guo Yan Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type Fixed Point Theory and Applications |
| title | Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type |
| title_full | Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type |
| title_fullStr | Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type |
| title_full_unstemmed | Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type |
| title_short | Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type |
| title_sort | weak convergence theorems of three iterative methods for strictly pseudocontractive mappings of browder petryshyn type |
| url | http://www.fixedpointtheoryandapplications.com/content/2008/672301 |
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