Asymmetric approximations in the space Lp(t)
Abstract
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.
Published
25.07.1999
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, https://umj.imath.kiev.ua/index.php/umj/article/view/4684.
Issue
Section
Research articles