An iterative approximation method for solving a general system of variational inequality problems and mixed equilibrium problems

作者：Wangkeeree Rabian^*; Kamraksa Uthai

来源：Nonlinear Analysis: Hybrid Systems , 2009, 3(4): 615-630.

DOI：10.1016/j.nahs.2009.05.005

• Nonexpansive mapping
• Cocoercive snapping
• General system of variational inequality
• Metric projection
• Strong convergence
• Fixed point
• Hilbert space

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general system of variational inequalities for a cocoercive mapping in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our results extend and improve the corresponding results of Ceng, Wang, and Yao [LC. Ceng, C.Y. Wang, J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res. 67 (2008) 375-3901, Ceng and Yao [LC. Ceng, J.C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems.). Comput. Appl. Math. doi:10.1016/j.cam.2007.02.022], Takahashi and Takahashi IS. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces.). Math. Anal. Appl. 331 (2007) 506-515] and many others.

• 出版日期2009-11