Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems

作者：Jaiboon C^*; Kumam P; Humphries U W

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2009, 32(2): 173-185.

• Extragradient method
• nonexpansive mapping
• k-Lipschitz continuous mapping
• variational inequality problem
• equilibrium problem
• fixed points

In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi [7].

• 出版日期2009