Banach空间中m-增生型非线性方程组的迭代解

摘要

Suppose E is an arbitrary real Banach space and T:D(T) E→E is a uniformly continuous m-accretive operator with bounded range,where the domain of T,D(T),is a proper subset of E.It is proved that for any given f∈E,the Ishikawa and the Mann iteration methods with errors introduced by L.S. Liu (J.Math.Anal.Appl.194(1995),114-125) converge strongly to the unique solution of the equation x+Tx＝f where T may not be Lipschitz.Our results extend and complement the recent results obtained by Chidume,Ding,Liu and Osilike.%设E为任意实Banach空间,T:D(T) E→E是具有有界值域的一致连续m-增生算子,其中T的定义域D(T)是E的一个子集.本文证明了当T不是Lipschitz连续时,对于任意给定的f∈E,含误差项的Ishikawa和Mann迭代方法(由刘立山教授提出,见J.Math.Anal.App.194(1995),114-125)强收敛于m-增生型非线性方程组x+Tx＝f的唯一解.本文改进和扩展了近期Chidume,Ding,Liu和Ostilike的许多相关结果.