A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces |
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Authors: | Xiaolong Qin Meijuan Shang Yongfu Su |
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Affiliation: | 1. Department of Mathematics, Gyeongsang National University, Chinju 660-701, Republic of Korea;2. Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China;3. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China |
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Abstract: | The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend the recent results of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515], Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43–52], Combettes and Hirstoaga [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 486–491], Iiduka and Takahashi, [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and many others. |
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Keywords: | 47H09 47H10 47H17 |
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