正则函数的修正的Cauchy型积分算子的不动点定理及迭代构造
In the first part of this paper, we discuss the Holder continuity of the cauchy integral operator for regular functions and the relation between ‖T[f] ‖α and ‖f‖α. In the second part of this paper, we introduce the modified cauchy integral operator T for regular functions. Firstly,we prove that the operator T has a unique fixed point by the Banach's Contraction Mapping Principle. Secondly, we give the Mann iterative sequence, and then we show the iterative sequence strongly converges to the fixed point of the operator T.
作 者： 王丽萍 彭维玲 肖卓峰 WANG Li Ping PENG Wei Ling XIAO Zhuo Feng 作者单位： 王丽萍,WANG Li Ping(School of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China)彭维玲,PENG Wei Ling(Department of Mathematics, Tonghua Teachers College, Jilin 134002, China)
肖卓峰,XIAO Zhuo Feng(Tibetan College of Hebei Normal University, Hebei 050091, China)
刊 名： 数学研究与评论 ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION 年，卷(期)： 2008 28(3) 分类号： O177.4 O177.91 关键词： real Clifford analysis regular function cauchy integral the fixed point manniteration