A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and stric...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/131890 |
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| _version_ | 1832564452577247232 |
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| author | Yekini Shehu |
| author_facet | Yekini Shehu |
| author_sort | Yekini Shehu |
| collection | DOAJ |
| description | We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth
and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature. |
| format | Article |
| id | doaj-art-1a6da89267c44daf9ec5888775d411d0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1a6da89267c44daf9ec5888775d411d02025-02-03T01:10:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/131890131890A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium ProblemsYekini Shehu0Mathematics Institute, African University of Science and Technology, Abuja, NigeriaWe construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.http://dx.doi.org/10.1155/2011/131890 |
| spellingShingle | Yekini Shehu A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems International Journal of Mathematics and Mathematical Sciences |
| title | A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
| title_full | A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
| title_fullStr | A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
| title_full_unstemmed | A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
| title_short | A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
| title_sort | new hybrid iterative scheme for countable families of relatively quasi nonexpansive mappings and system of equilibrium problems |
| url | http://dx.doi.org/10.1155/2011/131890 |
| work_keys_str_mv | AT yekinishehu anewhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems AT yekinishehu newhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems |