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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Bibliographic Details
Published in:Fixed Point Theory and Applications Vol. 2008; pp. 1 - 12
Main Authors: Takahashi, Wataru, Zembayashi, Kei
Format: Journal Article
Language:English
Japanese
Published: Springer Science and Business Media LLC 01.01.2008
SpringerOpen
Subjects:
Analysis
Applied mathematics. Quantitative methods
QA299.6-433
T57-57.97
ISSN:1687-1820, 1687-1812
Online Access:Get full text
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Summary: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.
ISSN:1687-1820
1687-1812
DOI:10.1155/2008/528476