The Fixed Point Theorem and the Iterative Approximation of Modified Cauchy Integral Operator of Regular Functions  

作　　者：WANG Li Ping PENG Wei Ling XIAO Zhuo Feng 

机构地区：[1]School of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China [2]Department of Mathematics, Tonghua Teachers College, Jilin 134002, China [3]Tibetan College of Hebei Normal University, Hebei 050091, China

出　　处：《Journal of Mathematical Research and Exposition》2008年第3期593-604,共12页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China （No. 10771049; 10771050）; the Natural Science Foundation of Hebei Province （No. A2007000225） and the Foundation of Hebei Normal University （No. L2007Q05）; the 11th Five-Year Plan Educational and Scientific Issues of Hebei Province （No. O8020147）.

摘　　要：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^-.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^-.

关 键 词：real Clifford analysis regular function cauchy integral the fixed point mann iteration. 

分 类 号：O177.4[理学—数学] O177.91[理学—基础数学]