A relaxed extragradient-like method for a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem

作者：Ceng, Lu-Chuan; Yao, Jen-Chih^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(3-4): 1922-1937.

DOI：10.1016/j.na.2009.09.033

• Strictly pseudocontractive mapping
• Fixed point
• Inverse-strongly-monotone mapping
• Variational inequality
• Generalized mixed equilibrium problem
• System of generalized equilibria

Very recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69 (2008) 1025-1033] suggested and analyzed an iterative method for finding a common solution of a generalized equilibrium problem and a fixed point problem of a nonexpansive mapping in a Hilbert space. In this paper, based on Takahashi-Takahashi's iterative method and well-known extragraidient method we introduce a relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space and then obtain a strong convergence theorem. Utilizing this theorem, we establish some new strong convergence results in fixed point problems, variational inequalities, mixed equilibrium problems and systems of generalized equilibria.

• 出版日期2010-2-1
• 单位上海大学; 中山大学; 上海师范大学