An iterative method of solution for equilibrium and optimization problems |
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Authors: | Yongfu Su Meijuan Shang Xiaolong Qin |
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Institution: | 1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;2. Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China |
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Abstract: | In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extended and improved the results of H. Iiduka and W. Takahashi Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and S. Takahashi and W. Takahashi Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. Therefore, by using the above result, an iterative algorithm for the solution of a optimization problem was obtained. |
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Keywords: | 74G10 47H09 47H10 |
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