Banach空间中广义变分不等式迭代算法的强收敛性

Strong Convergence of Iterative Algorithms for a Class of Generalized Variational Inequality Problems in Banach Spaces

利用修改的外梯度方法,结合修改的Mann迭代方法,讨论了一类Banach空间中严格伪压缩映像的广义变分不等式问题.在适当的条件下,证明了算法所得到的序列强收敛到相应问题的解.

In this paper, we disscuss a class of generalized variational inequality problems involved in strictly pseudo-contractive mapping in Banach spaces by using some new algorithms which couple modi- fied extra-gradient method with extended Mann iteration. It is proved that the sequences generated by the proposed iterative algorithms converge strongly to the solution of the generalized variational inequality problem. The results presented in this paper extend and improve some well-known results in the literature.