On stability of singular integral equation with Cauchy kernel with respect to integration path (Q2755686)

The authors discuss the following regular singular integral equation with Cauchy kernel NEWLINE\[NEWLINEa(t)\varphi(t)+ {b(t)\over \pi i} \int_\Gamma{\varphi(\tau)\over \tau-t} d\tau= f(t)\qquad (t\in\Gamma),NEWLINE\]NEWLINE where all functions satisfy Hölder conditions on the set \(E\), \(E\) is a bounded connected region on the plane and \(\Gamma(\subset E)\) is a smooth closed curve. When there are some smooth perturbations on \(\Gamma\), the stability of the above singular integral equation is investigated, an error estimate is given and a convergence theorem is established in the paper.