The Bojanov-Naidenov problem for the functions with non-symmetric restrictions on the oldest derivative

• Date: 2021
• Main Author: Кофанов, Володимир Олександрович
• Format: Article
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/254
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For given $r \in \NN$, $p, \alpha, \beta, \mu > 0$, we solve theextremal problems$$\int\nolimits_{a}^{b} x^q_{\pm}(t)dt \to \sup, \;\;\;\; q\ge p,\;$$on the set of pair $(x, I)$ functions $x\in L^r_{\infty}$ andintervals $I=[a,b] \subset \RR$ satisfying the inequalities $ -\beta\le x^{(r)...