2019
Том 71
№ 11

All Issues

Metelichenko A.B.

Articles: 1
Article (Russian)

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

Metelichenko A.B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 70-77

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 $f$.