On the Approximation by Modified Interpolation Polynomials in Spaces $L_p$

Abstract

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 $f$.