On the Approximation by Modified Interpolation Polynomials in Spaces L_p - Metelichenko, A.B. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
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.