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

  • E. G. Litvin
  • O. V. Polyakov Днепропетр. нац. ун-т


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 $L_{p(t)}$. We obtain inequalities of the type of duality relations.
How to Cite
Litvin, E. G., and O. V. Polyakov. “Asymmetric Approximations in the Space $L_{p(t)}$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 7, July 1999, pp. 952-9,
Research articles