Mirgand Sh. Shabozov, Mukim S. Saidusaynov, Mean-Square Approximation of Complex Variable Functions by Fourier Series in the Weighted Bergman Space, IJARM Volume 9, International Journal of Advanced Research in Mathematics (Volume 9) https://www.scipress.com/IJARM.9.34 Abstract: The problem of mean-square approximation of complex variables functions regularly in some simply connected domain<i> D </i>c C with Fourier series by orthogonal system when the weighted function <i>γ</i>: = <i>γ</i>(|<i>z|</i>) is nonnegative integrable in <i>D</i>, 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 of <i>m-th</i> order were obtained. An exact values of <i>n</i>-<i>widths</i> for specified class of functions were calculated. Keywords: Generalized Displacement Operator, Generalized Module of Continuity, Weighted Bergman Space