Iterative algorithms for hierarchical fixed points problems and variational inequalities

作者：Yao Yonghong; Cho Yeol Je^*; Liou Yeong Cheng

来源：Mathematical and Computer Modelling, 2010, 52(9-10): 1697-1705.

DOI：10.1016/j.mcm.2010.06.038

• Nonexpansive mappings
• Hierarchical fixed point problems
• Variational inequalities
• Iterative algorithms

This paper deals with a method for approximating a solution of the fixed point problem: find (x) over tilde is an element of H;(x) over tilde = (proj(F(T)) .S)(x) over tilde, where H is a Hilbert space, S is some nonlinear operator and T is a nonexpansive mapping on a closed convex subset C and proj(F(T)) denotes the metric projection on the set of fixed points of T. First, we prove a strong convergence theorem by using a projection method which solves some variational inequality. As a special case, this projection method also solves some minimization problems. Secondly, under different restrictions on parameters, we obtain another strong convergence result which solves the above fixed point problem.

• 出版日期2010-11
• 单位天津工业大学