Asymmetric approximations in the space $L_{p(t)}$

• Date: 1999
• Main Authors: Litvin, E. G., Polyakov, O. V., Литвин, Е. Г., Поляков, О. В
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4684
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which $$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$ where $p(t)$ is a positive measurable function. We establish a criterion for the element of the best $(α,β)$-approximation in the space $L...