摘要
设Ｘ是一致光滑Ｂａｎａｃｈ空间和Ｔ∶Ｄ（Ｔ）Ｘ→Ｘ是一（Ｌｉｐｓｃｈｉｔｚ）连续增殖算子，Ｄ（Ｔ）和Ｒ（Ｔ）分别表Ｔ的定义域和值域．对任意给定的ｆ∈Ｘ，由Ｓｘ＝－Ｔ＋ｆ，ｘ∈Ｄ（Ｔ），定义映象Ｓ∶Ｄ（Ｔ）→Ｘ．作者证明了，在适当条件下，关于Ｓ的Ｍａｎｎ迭代序列和Ｉｓｈｉｋａｗａ迭代序列强收敛于方程ｘ＋Ｔｘ＝ｆ的唯一解．相关结果研究了逼近方程ｘ－λＡｘ＝解的Ｍａｎｎ和Ｉｓｈｉｋａｗａ迭代序列的收敛性．其中ｆ∈Ｘ，λ＞０和Ａ∶Ｘ→Ｘ是（ＬｉｐｓｃｈｉｔＺ）连续耗散算子．
Let X be a uniformly smooth Banach sauce and T : D(T) X→ X be a(Lipschitz) continuous accretive operator with the domain D(T) and the range R(T).For any given f ∈ X, define S:D(T)→X by Sx=-Tx+ f. ∈D(T). We provethat the Mann and Ishikawa iterative sequences relating to S converge strongly to theunique solution of the equation x + Tx= f under suitable conditions. Some relatedresults deal with the convergence of Mann and Ishikawa iterative sequences forapproximating a solution of the equation x-λAx=f. where f ∈ X,λ> 0 and A : X→ X is B (Lipschitz) continuous dissipative operator.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
1996年第6期1-12,共12页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金
关键词
增殖算子方程
耗散算子方程
非线性
迭代法
解
Accretive operator equations, Dissipative operator equations, Iteration methods, Uniformly smooth Banach space
