非扩张映射和广义变分不等式的粘滞逼近法

Viscosity Approximation Methods for Nonexpansive Mappings and Generalized Variational Inequalities

应用已提出的非扩张映射的粘滞逼近方法,给定初值x_0∈C,考虑一般迭代过程{x_n},g(x_(n+1))=α_nf(x_n)+(1-α_n)SP_C(g(x_n)-λ_nAx_n),n≥0,其中{α_n}■(0,1),S:C→C是非扩张映射,C是实Hilbert空间H的非空闭凸子集.在{α_n}满足合适的条件下可证明,{x_n}强收敛到非扩张映射的不动点集和广义变分不等式解的公共元,且满足某变分不等式.

Viscosity approximation methods for nonexpansive mappings are studied. Consider the general iteration process {x_n},where x_0∈C is arbitrary and g（x_（n＋1））=α_nf（x_n）＋（1-α_n）SP_C（g（x_n）-λ_nAx_n）,S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H.It is shown that {x_n} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the Noor variational inequality for an inverse strongly monotone mapping which solves some variational inequality.