拟增生算子方程的广义最速下降逼近的收敛性  

Convergence of Generalized Steepest Descent Approximation to Quasl-accretive Operators Equations

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,绍兴312000

出　　处：《应用数学学报》2009年第1期143-153,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10271025);浙江省自然科学基金(Y606717)等资助项目.

摘　　要：证明了广义最速下降逼近强收敛于定义在一致光滑实Banach空间的真子集匕的局部有界拟增生算子的零点的一充要条件,相关的结果处理含φ-强拟增生算子的非线性方程迭代解的收敛性.所得的结果推广和统一如Xu和Roach,Xu、Zhang和Roach,Chidume,Zegeye和Ntatin,徐宗本和蒋耀林,Chidume,Zhou等人的相应结果.A necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of quasi-accretive locally bounded operators defined on proper subsets of uniformly smooth real Banach space. Related results deal with the strongly convergence of the scheme to a solution of equations involving φ-strongly quasiaccretive operators. These results extend and unify corresponding ones by Xu and Roach, Xu Zhongben and Jiang Yaolin, Chidume, Xu, Zhang and Roach, Zhou and others.

关 键 词：拟增生算子 Φ-强增生算子 广义最速下降逼近 一致光滑实Banach空间 局部有界算子 充要条件 

分 类 号：O177.91[理学—数学]