Banach空间中增生算子方程迭代法与非线性收缩半群弱收敛的充要条件

A Necessary and Sufficient Condit ion for Weak Convergence of Iterative Methodsfor Accretive Operators and of Nonlinear Contraction Semigroups in Banach Spaces

本文在条件（Ｉ）下，证明了增生算子最速下降法和预解式迭代法弱收敛于零点的充要条件，以及非线性收缩半群弱收敛于平衡点的充要条件．所获结果推广了［１］中的基本定理，并与［２］所获得的相应强收敛充要条件对应．

A necessary and sufficient condition is presented which ensures the weak convergenceof the steepest descent and the resolvent iterations to accretive operators and of the contractionsemigroups in Banach spaces.The conclusion, which can be regarded as a weakly topologicalversion of the theorem established in[2] , generalizes and improves on those results proved in[1].