TY - JOUR AU - O. G. Rovenska AU - V. V. Savchuk AU - M. V. Savchuk PY - 2022/06/17 Y2 - 2024/03/28 TI - Approximation of holomorphic functions by Cesàro means JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 74 IS - 5 SE - Research articles DO - 10.37863/umzh.v74i5.7143 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7143 AB - UDC 517.5For the Lipschitz class of functions holomorphic in the disc, we present a constructive characterization of this class in terms of Cesaro’s means of order $\alpha \ge 2$ of the Taylor series. We solve the problem of exact upper bound for the deviations of Cesaro’s means of order $\alpha \ge 2$ as well as for the deviations of Riesz’s means of order 2 of the Taylor series in the class of functions holomorphic in the disc and having a bounded derivative.  ER -