Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings
<p/> <p>Let <inline-formula><graphic file="1687-1812-2005-359216-i1.gif"/></inline-formula> be a nonempty closed convex subset of a reflexive real Banach space <inline-formula><graphic file="1687-1812-2005-359216-i2.gif"/></inline-form...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2005/359216 |
| _version_ | 1818743259432747008 |
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| author | Shahzad Naseer Chidume CE Zegeye Habtu |
| author_facet | Shahzad Naseer Chidume CE Zegeye Habtu |
| author_sort | Shahzad Naseer |
| collection | DOAJ |
| description | <p/> <p>Let <inline-formula><graphic file="1687-1812-2005-359216-i1.gif"/></inline-formula> be a nonempty closed convex subset of a reflexive real Banach space <inline-formula><graphic file="1687-1812-2005-359216-i2.gif"/></inline-formula> which has a uniformly Gâteaux differentiable norm. Assume that <inline-formula><graphic file="1687-1812-2005-359216-i3.gif"/></inline-formula> is a sunny nonexpansive retract of <inline-formula><graphic file="1687-1812-2005-359216-i4.gif"/></inline-formula> with <inline-formula><graphic file="1687-1812-2005-359216-i5.gif"/></inline-formula> as the sunny nonexpansive retraction. Let <inline-formula><graphic file="1687-1812-2005-359216-i6.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2005-359216-i7.gif"/></inline-formula>, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of <inline-formula><graphic file="1687-1812-2005-359216-i8.gif"/></inline-formula> has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that <inline-formula><graphic file="1687-1812-2005-359216-i9.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2005-359216-i10.gif"/></inline-formula>, satisfy some mild conditions.</p> |
| first_indexed | 2024-12-18T02:25:34Z |
| format | Article |
| id | doaj.art-8ce8327e3cf942caa0c3d8c24d68a3bc |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-18T02:25:34Z |
| publishDate | 2005-01-01 |
| publisher | SpringerOpen |
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| series | Fixed Point Theory and Applications |
| spelling | doaj.art-8ce8327e3cf942caa0c3d8c24d68a3bc2022-12-21T21:24:03ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122005-01-0120052359216Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappingsShahzad NaseerChidume CEZegeye Habtu<p/> <p>Let <inline-formula><graphic file="1687-1812-2005-359216-i1.gif"/></inline-formula> be a nonempty closed convex subset of a reflexive real Banach space <inline-formula><graphic file="1687-1812-2005-359216-i2.gif"/></inline-formula> which has a uniformly Gâteaux differentiable norm. Assume that <inline-formula><graphic file="1687-1812-2005-359216-i3.gif"/></inline-formula> is a sunny nonexpansive retract of <inline-formula><graphic file="1687-1812-2005-359216-i4.gif"/></inline-formula> with <inline-formula><graphic file="1687-1812-2005-359216-i5.gif"/></inline-formula> as the sunny nonexpansive retraction. Let <inline-formula><graphic file="1687-1812-2005-359216-i6.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2005-359216-i7.gif"/></inline-formula>, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of <inline-formula><graphic file="1687-1812-2005-359216-i8.gif"/></inline-formula> has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that <inline-formula><graphic file="1687-1812-2005-359216-i9.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2005-359216-i10.gif"/></inline-formula>, satisfy some mild conditions.</p>http://www.fixedpointtheoryandapplications.com/content/2005/359216 |
| spellingShingle | Shahzad Naseer Chidume CE Zegeye Habtu Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings Fixed Point Theory and Applications |
| title | Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| title_full | Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| title_fullStr | Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| title_full_unstemmed | Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| title_short | Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| title_sort | convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings |
| url | http://www.fixedpointtheoryandapplications.com/content/2005/359216 |
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