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+; \( D_ρ = σ (x)d^2d x^2+τ (x)dd x \) , σ and τ are polynomials of at most the second and first degrees, respectively, ρ is a weight function, 0 < p ≤ 2, 0 < h