Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces
Let E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpans...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/285376 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550320320806912 |
|---|---|
| author | Yekini Shehu Jerry N. Ezeora |
| author_facet | Yekini Shehu Jerry N. Ezeora |
| author_sort | Yekini Shehu |
| collection | DOAJ |
| description | Let E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a
nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpansive
mapping T:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite
family of m-accretive mappings of K to E. As a consequence, an iterative scheme is constructed to converge to
a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from K to E under certain mild conditions. |
| format | Article |
| id | doaj-art-fcfc8897812b4a819f30413ef0cb0142 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fcfc8897812b4a819f30413ef0cb01422025-02-03T06:07:06ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/285376285376Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach SpacesYekini Shehu0Jerry N. Ezeora1Department of Mathematics, University of Nigeria, Nsukka, NigeriaMathematics Institute, African University of Science and Technology, Abuja, NigeriaLet E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpansive mapping T:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite family of m-accretive mappings of K to E. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from K to E under certain mild conditions.http://dx.doi.org/10.1155/2010/285376 |
| spellingShingle | Yekini Shehu Jerry N. Ezeora Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces |
| title_full | Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces |
| title_fullStr | Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces |
| title_full_unstemmed | Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces |
| title_short | Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces |
| title_sort | path convergence and approximation of common zeroes of a finite family of m accretive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2010/285376 |
| work_keys_str_mv | AT yekinishehu pathconvergenceandapproximationofcommonzeroesofafinitefamilyofmaccretivemappingsinbanachspaces AT jerrynezeora pathconvergenceandapproximationofcommonzeroesofafinitefamilyofmaccretivemappingsinbanachspaces |