Hilbert空间中逼近算子不动点的几何结果

Geometric Results for Approximating Fixed Points of Operators in Hilbert Spaces

设E是Hilbert空间,T是E中具非空不动点集F(T)的非线性映象,许多非线性映像的多种形式的迭代序列{xn}可逼近映像T的不动点p0∈F(T).并且逼近过程{xn}与不动点集F(T)有如下的钝角关系limsupn→+∞〈p-p0,‖xxnn--pp00‖〉0,p∈F(T).证明了一般非线性映像不动点逼近过程的这种几何结果,并应用这个结果研究了具误差Ishikawa迭代逼近非扩张映像不动点的钝角关系.

Let E be a Hilbert space,T be a nonlinear mapping with nonempty set of fixed points. For a lot of nonlinear mappings,the fixed points can be approximated by iteration sequence （xn）. In the approximating process ,a geometric result,which is obtuse relation,can be expressed as follows lim sup n→＋∞〈p-p0,xn-p0/｜｜xn-p0｜｜〉≤0,A↓p∈F（T）.In the relevant condition,the geometric result holds for a lot of nonlinear mappings. This geometric result is proved for some nonlinear mappings. In particular, this geometric result for Ishikawa iteration with errors of nonexpansive mapping is proved.