On the Approximation by Modified Interpolation Polynomials in Spaces $L_p$
We consider certain modified interpolation polynomials for functions from the space $L_p \;[0, 2π], 1 ≤ p ≤ ∞$. An estimate for the rate of approximation of an original function f by these polynomials in terms of its modulus of continuity is obtained. We establish that these polynomials converge almost everywhere to $f$.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 1, pp 86–95.
Citation Example: Metelichenko A.B. On the Approximation by Modified Interpolation Polynomials in Spaces $L_p$ // Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 70-77.