A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces
<p/> <p>We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate set...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/572156 |
| Summary: | <p/> <p>We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.</p> |
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| ISSN: | 1687-1820 1687-1812 |