Bojanov–Naidenov problem for differentiable functions and the Erdös problem for polynomials and splines

• Date: 2023
• Main Authors: Kofanov, V., Кофанов, Владимир Александрович, Кофанов, Володимир
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2023
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7259
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We solve the extremal problem $$\big\|x^{(k)}_{\pm}\big\|_{L_p[a, b]} \to \sup, \quad k=0,1,\ldots ,r-1,\quad p > 0 ,$$ in the class of pairs $(x, I)$ of functions $x\in S^k_{\varphi}$ such that $ \varphi^{(i)} $ are the comparison function...