Asymmetric approximations in the space $L_{p(t)}$ - Litvin, E. G.; Polyakov, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which$$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< ∞ }$$ 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.