Hilbert空间中非扩张映射的广义隐粘性迭代方法

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

在Hilbert空间框架下,给出并研究了非扩张映射的一类广义的隐粘性迭代方法,在合适的条件下,证明了迭代程序所生成的序列强收敛到非扩张映射的不动点,并且该不动点还是某变分不等式的解.结果是新的,推广和改进了一些最新的结论.

The purpose of this paper is to introduce and study the general viscosity approximation methods for the implicit rule of nonexpansive mappings in the setting of infinitedimensional Hilbert spaces.Under suitable conditions,A strong converge theorem to a fixed point of the nonexpansive mapping is proved.Also,it is shown that the limit solves an additional variational inequality.The results presented in this paper are new which extend and improve some recent results.