The Lower Estimate for Bernstein Operator

Gal, Sorin G.; Tachev, Gancho T.

The Lower Estimate for Bernstein Operator

Gal, Sorin G.; Tachev, Gancho T.

Mathematica Balkanica New Series (2013)

Volume: 27, Issue: 1-2, page 39-51
ISSN: 0205-3217

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Abstract

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MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.

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Gal, Sorin G., and Tachev, Gancho T.. "The Lower Estimate for Bernstein Operator." Mathematica Balkanica New Series 27.1-2 (2013): 39-51. <http://eudml.org/doc/281468>.

@article{Gal2013,
abstract = {MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.},
author = {Gal, Sorin G., Tachev, Gancho T.},
journal = {Mathematica Balkanica New Series},
keywords = {Bernstein polynomials; lower estimate; Ditzian-Totik modulus of smoothness; K-functional},
language = {eng},
number = {1-2},
pages = {39-51},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {The Lower Estimate for Bernstein Operator},
url = {http://eudml.org/doc/281468},
volume = {27},
year = {2013},
}

TY - JOUR
AU - Gal, Sorin G.
AU - Tachev, Gancho T.
TI - The Lower Estimate for Bernstein Operator
JO - Mathematica Balkanica New Series
PY - 2013
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 27
IS - 1-2
SP - 39
EP - 51
AB - MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.
LA - eng
KW - Bernstein polynomials; lower estimate; Ditzian-Totik modulus of smoothness; K-functional
UR - http://eudml.org/doc/281468
ER -

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