The fixed point and Mann iterative of a kind of higher order singular Teodorescu operator. (English) Zbl 1327.30060

Summary: First, we discuss the Hölder continuity for a kind of higher order singular Teodorescu operator in \(R^n\) and estimate its norm. Next, we introduce a modified higher order Teodorescu operator \(T^\ast_\Omega\) and show that the operator \(T^\ast_\Omega\) 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 \(T^\ast_\Omega\) and gives an iterative sequence of the solution of a kind of singular integral equation.


30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
45E05 Integral equations with kernels of Cauchy type
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