变分不等式与非扩张映象公共解的三步迭代算法

Three-step iterative algorithms for variational inequalities and nonexpansive mappings

作者在Hilbert空间中引入并研究了一类隐拟变分不等式。利用投影技术,作者得到了这类隐拟变分不等式解的存在性,并给出了三步迭代算法,然后证明了由算法生成的迭代序列收敛于三个非扩张映象公共不动点集与变分不等式问题解集的公共点。

In this paper, a class of implicit quasi-variational inequalities in Hilbert spaces is studied. Using projection technique, the existence of solutions for the implicit quasi-variational inequalities is obtained, and a new three-step iterative algorithm is constructed for solving it. It is proved that the iteratire sequences generated by the algorithm is convergent to the common element of the set of common fixed points of three nonexpansive mappings and the solutions set of the implicit quasi-variational inequalities.