Hilbert空间中非扩张映射隐中点规则的粘性逼近方法

Viscosity Approximation Methods for the Implicit Midpoint Rule of Nonexpansive Mappings in Hilbert Spaces

在Hilbert空间框架下,对非扩张映射引入了一个新的隐中点规则的粘性逼近迭代程序,在合适的参数条件下,证明了该迭代程序生成的序列的强收敛性,同时也证明了隐中点规则生成的序列的极限也是变分不等式问题的解.

The implicit midpoint rule of nonexpansive mappings in Hilbert spaces was introduced. The strong convergence of this method was proved under certain assumptions imposed on the sequence of parameters. Moreover, it is shown that the limit of the sequence generated by the implicit midpoint rule solves an additional variational inequality.