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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Institution: | 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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