The fixed point and Mann iterative of a kind of higher order singular Teodorescu operator
Heju Yang, Xiang-Hui Zhao · Complex Variables and Elliptic Equations · 2015
First, we discuss the Hölder continuity for a kind of higher order singular Teodorescu operator in and estimate its norm. Next, we introduce a modified higher order Teodorescu operator and show that the operator has a unique fixed point by the Banach’s Contraction Mapping Principle. Finally, we prove that the Mann iterative sequence strongly converges to the fixed point of and gives an iterative sequence of the solution of a kind of singular integral equation.