Minimum-Norm Fixed Point of Pseudocontractive Mappings
Let K be a closed convex subset of a real Hilbert space H and let be a continuous pseudocontractive mapping. Then for and each , there exists a sequence satisfying which converges strongly, as , to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which conver...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/926017 |
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| _version_ | 1832553342601003008 |
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| author | Habtu Zegeye Naseer Shahzad Mohammad Ali Alghamdi |
| author_facet | Habtu Zegeye Naseer Shahzad Mohammad Ali Alghamdi |
| author_sort | Habtu Zegeye |
| collection | DOAJ |
| description | Let K be a closed convex subset of a real Hilbert space H and let be a continuous pseudocontractive mapping. Then for and each , there exists a sequence satisfying which converges strongly, as , to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction. |
| format | Article |
| id | doaj-art-8c2442c867cd4f9db7d1bd9fe085f627 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8c2442c867cd4f9db7d1bd9fe085f6272025-02-03T05:54:21ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/926017926017Minimum-Norm Fixed Point of Pseudocontractive MappingsHabtu Zegeye0Naseer Shahzad1Mohammad Ali Alghamdi2Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, BotswanaDepartment of Mathematics, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi ArabiaLet K be a closed convex subset of a real Hilbert space H and let be a continuous pseudocontractive mapping. Then for and each , there exists a sequence satisfying which converges strongly, as , to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.http://dx.doi.org/10.1155/2012/926017 |
| spellingShingle | Habtu Zegeye Naseer Shahzad Mohammad Ali Alghamdi Minimum-Norm Fixed Point of Pseudocontractive Mappings Abstract and Applied Analysis |
| title | Minimum-Norm Fixed Point of Pseudocontractive Mappings |
| title_full | Minimum-Norm Fixed Point of Pseudocontractive Mappings |
| title_fullStr | Minimum-Norm Fixed Point of Pseudocontractive Mappings |
| title_full_unstemmed | Minimum-Norm Fixed Point of Pseudocontractive Mappings |
| title_short | Minimum-Norm Fixed Point of Pseudocontractive Mappings |
| title_sort | minimum norm fixed point of pseudocontractive mappings |
| url | http://dx.doi.org/10.1155/2012/926017 |
| work_keys_str_mv | AT habtuzegeye minimumnormfixedpointofpseudocontractivemappings AT naseershahzad minimumnormfixedpointofpseudocontractivemappings AT mohammadalialghamdi minimumnormfixedpointofpseudocontractivemappings |