Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 563-587
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M. K. Potapov; F. M. Berisha. On the connection between a $r$-order modulus of smoothness and the best approximation by algebraic polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 563-587. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/
@article{FPM_1999_5_2_a12,
author = {M. K. Potapov and F. M. Berisha},
title = {On the connection between a~$r$-order modulus of smoothness and the~best approximation by algebraic polynomials},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {563--587},
year = {1999},
volume = {5},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/}
}
TY - JOUR
AU - M. K. Potapov
AU - F. M. Berisha
TI - On the connection between a $r$-order modulus of smoothness and the best approximation by algebraic polynomials
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1999
SP - 563
EP - 587
VL - 5
IS - 2
UR - http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/
LA - ru
ID - FPM_1999_5_2_a12
ER -
%0 Journal Article
%A M. K. Potapov
%A F. M. Berisha
%T On the connection between a $r$-order modulus of smoothness and the best approximation by algebraic polynomials
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1999
%P 563-587
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/
%G ru
%F FPM_1999_5_2_a12
In this paper an asymmetrical operator of generalized translation is introduced and used to define the generalized modulus of smoothness; the direct and inverse theorems in approximation theory are proved for that modulus.
