Generalization of the Schwarz–Pick inequality and its application to the extreme problems of approximation of holomorphic functions

• Date: 2025
• Main Authors: Savchuk, V., Savchuk, M., Савчук, Віктор Васильович, Савчук, Віктор, Савчук, Марина
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2025
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8692
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We propose a method for the pointwise estimation of the derivative \[\left(\frac{f(z)-S_n(f)(z)}{z^n}\right)',\quad n\in\mathbb Z_+,\] where $S_n(f)$ is a partial sum of the Taylor series of a bounded holomorphic function in the unit circle $\mathbb D$ in terms of the absolute val...