an:06830725
Zbl 1389.30160
Yang, Heju; Li, Zunfeng; Guo, Bingchan
\({L^p}\) integrability of a higher order Teodorescu operator in Clifford analysis
ZH
Appl. Math., Ser. A (Chin. Ed.) 32, No. 2, 189-197 (2017).
00373533
2017
j
30G35
Clifford analysis; Teodorescu operator; fixed point theorem
Summary: Firstly, the \(A_n\left(R \right)\)-valued higher order Teodorescu operator \(T\) in \(\mathbb R^n\) is defined and its properties in \(L^\gamma\) space are discussed. Secondly, its norm is estimated and a modified higher order Teodorescu operator \(T^*\) is introduced. And then, that the operator \(T^*\) has a unique fixed point by the Banach's contract mapping principle is proved. Finally, that the Mann iterative sequence strongly converges to the fixed point of \(T^*\) is proved and an iterative sequence of the solution of a singular integral equation is given.