In this paper, we consider the problem of mean-square approximation of complex variables functions which are regular in the unit disk of the complex plane. We obtain sharp estimates of the value of the best approximation by algebraic polynomials in terms of K-functionals. Exact values of some widths of the specified class of functions are calculated.

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The problem of mean-square approximation of complex variables functions regularly in some simply connected domainDc C with Fourier series by orthogonal system when the weighted functionγ: =γ(|z|) is nonnegative integrable inD, was considered. An exact convergence rate of Fourier series by orthogonal system of functions on some class of functions given by special module of continuity ofm-thorder were obtained. An exact values ofn-widthsfor specified class of functions were calculated.