| The Fixed Point and Mann Iteration of a Modified Isotonic Operator |
| Received:July 30, 2012 Revised:June 04, 2013 |
| Key Words:
Clifford analysis isotonic operator the fixed point theorem Mann iteration.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10771049; 11171349) and the Science Foundation of Hebei Province (Grant No.A2010000346). |
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| Abstract: |
| 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 $T'$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.05.008 |
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