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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 |
| Institution: | 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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