Application of Faber polynomials to the approximate solution of a generalized boundary value problem of linear conjugation in the theory of analytic functions

In the present paper the method of successive approximations and Faber polynomials are used to derive the approximate solution of a generalized boundary value problem of linear conjugation on the Lyapunov curve. The conditions for the existence and uniqueness of the solution are presented in the L2L2 and H(α)H(α) spaces.