修正的isotonic算子的不动点与Mann迭代

The Fixed Point and Mann Iteration of a Modified Isotonic Operator

中文关键词:  Clifford分析  isotonic算子  不动点定理  Mann迭代序列.

英文关键词:Clifford analysis  isotonic operator  the fixed point theorem  Mann iteration.

中文摘要:

      在论文的第一部分, 研究与讨论了isotonic函数的Cauchy型奇异积分算子$T$的 H\"{o}lder连续性及$\|T[f]\|_{\alpha}$与$\|f\|_{\alpha}$间的关系. 在第二部分, 引入了isotonic函数的修正的Cauchy型奇异积分算子$T'$, 首先利用压缩不动点定理证明此修正的Cauchy型奇异积分算子$T'$存在唯一不动点, 然后给出其不动点的Mann迭代序列并证明此序列强收敛于$T'$算子的不动点.

英文摘要:

      This paper consists of two parts. In the first part, we discuss the H\"{o}lder continuity of Cauchy-type integral operator $T$ of isotonic functions and the relationship between $\|T[f]\|_{\alpha}$ and $\|f\|_{\alpha}$. In the second part, firstly, we introduce a modified Cauchy-type integral operator $T'$ and demonstrate that the operator $T'$ has a unique fixed point by the Contraction Mapping Principle. Then we give the Mann iterative sequence and prove that the Mann iterative sequence strongly converges to the fixed point of the modified Cauchy-type integral operator $T'$.