On the Best Approximation in the Mean by Algebraic Polynomials with Weight and the Exact Values of Widths for the Classes of Functions - Vakarchuk, S. B.; Shvachko, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
The exact value of the extremal characteristic is obtained on the class L 2 r (D ρ ), where r ∈ ℤ+; \( D_{ρ} = σ (x)\frac{d^2}{d{ x}^2}+τ (x)\frac{d}{d x} \) , σ and τ are polynomials of at most the second and first degrees, respectively, ρ is a weight function, 0 < p ≤ 2, 0 < h