分层不动点及变分不等式的一种粘性迭代方法

A viscosity iteration mothod for hierarchical fixed point and variational inequalities

设H是一实Hilbert空间,设{Tn}:H→H是一可数族的非扩张映像,且M:=∩∞n=1F(Tn)≠φ.求解了一可数族非扩张映像{Tn}关于另一非扩张映像S:H→H之一公共不动点,即是求一x*∈M,使得〈x*-Sx*,x*-x〉≤0,x∈M.

Let H be a real Hilbert space, { Tn } ：H→H be a countable family of nonexpansive mappings,and M：=∞∩n=1F（Tn）≠φ.The solutions of the countable family of nonexpansive mappings { Tn } are sought in the set of the fixed points of another nonexpan- sive mapping S：H→H, that is to find an x^＊∈M, such that 〈x^＊-Sx^＊,x^＊-x〉≤0,Ax∈M.