Strong convergence of composite iterative methods for equilibrium problems and fixed point problems |
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Authors: | Jong Soo Jung |
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Affiliation: | Department of Mathematics, Dong-A University, Hadan-Dong 840, Saha-Gu, Busan 604-714, Republic of Korea |
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Abstract: | We introduce a new composite iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping. Our results substantially improve the corresponding results of Takahashi and Takahashi [A. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. Essentially a new approach for finding solutions of equilibrium problems and the fixed points of nonexpansive mappings is provided. |
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Keywords: | Composite iterative scheme Viscosity approximation method Equilibrium problem Fixed point Nonexpansive mapping Variational inequality |
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