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

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• 作者：Lu-Chuan Ceng ; Jen-Chih Yao
• 关键词：Strictly pseudocontractive mapping ; Fixed point ; Inverse-strongly-monotone mapping ; Variational inequality ; Generalized mixed equilibrium problem ; System of generalized equilibria
• 刊名：Nonlinear Analysis
• 出版年：2010
• 出版时间：1 February 2010
• 年：2010
• 卷：72
• 期：3-4
• 页码：1922-1937
• 全文大小：978 K

文摘

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 extragradient 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.