An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces
We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that conv...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/504503 |
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| _version_ | 1832568300956024832 |
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| author | H. Zegeye N. Shahzad |
| author_facet | H. Zegeye N. Shahzad |
| author_sort | H. Zegeye |
| collection | DOAJ |
| description | We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. |
| format | Article |
| id | doaj-art-8d597c257fa54fcdbfd2f044db6ab881 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8d597c257fa54fcdbfd2f044db6ab8812025-02-03T00:59:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/504503504503An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach SpacesH. Zegeye0N. Shahzad1Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, BotswanaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.http://dx.doi.org/10.1155/2012/504503 |
| spellingShingle | H. Zegeye N. Shahzad An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces Journal of Applied Mathematics |
| title | An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces |
| title_full | An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces |
| title_fullStr | An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces |
| title_full_unstemmed | An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces |
| title_short | An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces |
| title_sort | iteration to a common point of solution of variational inequality and fixed point problems in banach spaces |
| url | http://dx.doi.org/10.1155/2012/504503 |
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