Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings

We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution o...

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Vydané v:Fixed Point Theory and Applications Ročník 2008; s. 1 - 12
Hlavní autori: Takahashi, Wataru, Zembayashi, Kei
Médium: Journal Article
Jazyk:English
Japanese
Vydavateľské údaje: Springer Science and Business Media LLC 01.01.2008
SpringerOpen
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Analysis
Applied mathematics. Quantitative methods
QA299.6-433
T57-57.97
ISSN:1687-1820, 1687-1812
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Abstract We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.
AbstractList We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.
Author Kei Zembayashi
Wataru Takahashi
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Snippet We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a...
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QA299.6-433
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Title Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings
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