Banach空间中单参数非扩张半群不动点和变分不等式解的粘性逼近方法

Viscosity Approximation Methods for the Fixed-point of the One-parameter Nonexpansive Semigroups and the Solutions of Variational Inequalities in Banach Spaces

研究单参数非扩张半群的不动点和某变分不等式的解的迭代算法.在具有弱序列连续对偶映射的Banach空间中,利用粘性逼近方法,建立非扩张半群的不动点的三步迭代格式,证明该方法所得到的序列在一定条件下是强收敛的,并收敛于某变分不等式的唯一解.所得结论推广和统一了一些类似文献的结论.

The iterative scheme of the fixed point for the one-parameter nonexpansive semigroups and the solution for a certain variational inequality is introduced in this paper. In the real Banach space with weakly sequentially continuous duality mapping,utilizing the viscosity approximation method,the three-step iterative format of fixed point concerning the nonexpansive semigroups is established and the strong convergence theorems of the iterative sequences are obtained under certain conditions. And the fixed point is exactly the unique solution of certain variational inequalities. The results presented in this paper extend and unify most of the results that have been proposed for this class of nonlinear mappings.