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Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces |
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| Authors: | Xiaolong Qin Meijuan Shang Haiyun Zhou |
| Affiliation: | aDepartment of Mathematics, Gyeongsang National University, Chinju 660-701, Republic of Korea bDepartment of Mathematics, Shijiazhuang University, Shijiazhuang 050035, PR China cDepartment of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China |
| Abstract: | In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350], Yao and Yao [Y.H. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] and Many others. |
| Keywords: | Projection method Relaxed cocoercive mapping Nonexpansive mapping Fixed point |
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