An implicit iterative scheme for monotone variational inequalities and fixed point problems

作者：Ceng, L C; Cubiotti, R; Yaoc, J C^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 69(8): 2445-2457.

DOI：10.1016/j.na.2007.08.023

• variational inequality
• nonexpansive mapping
• implicit iterative scheme
• monotone mapping
• fixed point
• weak convergence
• demiclosedness principle
• opial's condition

In this paper we introduce an implicit iterative scheme for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The implicit iterative scheme is based on two well-known methods: extragradient and approximate proximal. We obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme. On the basis of this theorem, we also construct an implicit iterative process for finding a common fixed point of N 1 mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other N mappings are nonexpansive.

• 出版日期2008-10-15
• 单位中山大学; 上海师范大学