A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces |
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Authors: | Somyot Plubtieng Rattanaporn Punpaeng |
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Affiliation: | Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand |
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Abstract: | In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others. |
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Keywords: | Equilibrium problem Viscosity approximation method Nonexpansive mapping Minimization problem Fixed point |
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