Approximate solution of a dominant singular integral equation with conjugation

D. Pylak; P.  Wójcik

doi:10.37863/umzh.v73i9.758

D. Pylak Lublin Univ. Technology, Poland
P. Wójcik Lublin Univ. Technology, Poland

DOI: https://doi.org/10.37863/umzh.v73i9.758

Keywords: singular integral equations Cauchy kernel successive approximation

Abstract

UDC 517.5
In the present paper, the method of successive approximations and Faber polynomials are used to derive an approximate solution of a dominant singular integral equation with Holder continuous coefficients and conjugation on the Lyapunov curve.
Moreover, conditions of convergence in the $L_2$ and $H(α)$ spaces are presented.

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