非扩张半群的变分不等式的不动点解的粘性逼近方法
VISCOSITY APPROXIMATION METHODS FOR THE FIXED-POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS

本文研究了非扩张半群的变分不等式的不动点解的迭代算法.利用变分不等式与不动点问题的解的关系,结合粘性逼近方法,建立了非扩张半群的不动点的两步迭代格式,证明了该方法所得到的迭代序列在一定条件下的强收敛性,并收敛于某变分不等式的唯一解.
The iterative scheme of fixed point solutions to variational inequalities of nonexpansive semigroups is researched in the real Banach space with a uniformly Gateaux differentiable normin this paper. Utilizing the relationship between the variational inequalities and fixed point solution, together with the approach of viscosity approximation, we establish the two-step iterative format of fixed point concerning the nonexpansive semigroups and prove the iterative sequences obtained by this approach possess strong convergence under certain conditions and will strongly converge to the unique solution of certain variational inequality