扰动m-增生算子方程的Ishikawa迭代程序  

Ishikawa Iterative Process with Errors for Perturbed m-Accretive Operator Equations

作　　者：沈自飞[1] 杨敏波[1] 

机构地区：[1]浙江师范大学数学系

出　　处：《数学学报（中文版）》2005年第4期801-808,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10471113);浙江省自然科学基金资助项目(M103098)

摘　　要：设X是光滑Banach空间,A:X→X是一致连续的m-增生算子,S:X→X是一致连续的φ--强增生算子,本文证明实光滑Banach空间上连续的m-增生算子是单值的且具误差的Ishikawa和Mann迭代序列强收敛到方程z=Sx+λAx的唯一解,其中z∈X,λ≥0.我们的结果改进和推广了近期文献中的相应结果.Let X be a smooth Banach space, A : X→X a uniformly continuous m-accretive operator, S: X→X a uniformly continuous φ-accretive operator. It is proved that a continuous m-accretive operator on a real smooth Banach space is single-valued and the Ishikawa and Mann iterative processes with errors converge strongly to the unique solution of the equation z=Sx+λAx for given z∈X and λ≥0. Our results improve and generalize some recent results in the literature greatly.

关 键 词：M-增生算子 Φ-强增生算子 Ishikawa和Mann迭代 

分 类 号：O177.91[理学—数学]