Approximation of cauchy-type integrals in Jordan domains

Abstract

The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis of the Faber polynomials after the summation of Faber series. Analogs of the author's results are obtained for the classes $L_{\beta}^{\psi} \mathfrak{R}$