An extragradient-like approximation method for variational inequality problems and fixed point problems

作者：Ceng, Lu Chuan; Yao, Jen Chih^*

来源：Applied Mathematics and Computation, 2007, 190(1): 205-215.

DOI：10.1016/j.amc.2007.01.021

• extragradient-like approximation method
• variational inequality
• fixed point
• monotone mapping
• nonexpansive mapping
• strong convergence

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a non-expansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish a strong convergence theorem for two iterative sequences generated by this method.

• 出版日期2007-7-1
• 单位上海师范大学; 中山大学