On stability of Cauchy-type integral with kernel density of class H* with respect to path of integration for an open arc

Abstract

In this article, as the integral path is an open arc, we discuss the stability of a Cauchy-type integral with kernel density of class H* when a perturbation of the integral path occurs. And we discuss the stability of the Cauchy kernel singular integral with a kernel density of class H* when a perturbation of the integral path occurs.

Cauchy-type integral:

• Open arc
• Smooth perturbation curve
• Stability

AMS Subject Classifications::

• 30E20
• 30E25

Acknowledgements

This work was supported by Natural Science Foundation of China (10071016), the Natural Science Foundation of Fujian Province (Z0511013) and the Science and Technology Foundation of the Education Department of Fujian Province (JA06074), China.