# Approximation of functions from ${L}^{p}{\left(\omega \right)}_{\beta}$ by general linear operators of their Fourier series

Włodzimierz Łenski; Bogdan Szal

Banach Center Publications (2011)

- Volume: 95, Issue: 1, page 339-351
- ISSN: 0137-6934

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topWłodzimierz Łenski, and Bogdan Szal. "Approximation of functions from $L^{p}(ω)_{β}$ by general linear operators of their Fourier series." Banach Center Publications 95.1 (2011): 339-351. <http://eudml.org/doc/282506>.

@article{WłodzimierzŁenski2011,

abstract = {We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of S. Lal [Appl. Math. Comput. 209 (2009), 346-350].},

author = {Włodzimierz Łenski, Bogdan Szal},

journal = {Banach Center Publications},

keywords = {rate of approximation; summability of Fourier series; Lipschitz classes},

language = {eng},

number = {1},

pages = {339-351},

title = {Approximation of functions from $L^\{p\}(ω)_\{β\}$ by general linear operators of their Fourier series},

url = {http://eudml.org/doc/282506},

volume = {95},

year = {2011},

}

TY - JOUR

AU - Włodzimierz Łenski

AU - Bogdan Szal

TI - Approximation of functions from $L^{p}(ω)_{β}$ by general linear operators of their Fourier series

JO - Banach Center Publications

PY - 2011

VL - 95

IS - 1

SP - 339

EP - 351

AB - We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of S. Lal [Appl. Math. Comput. 209 (2009), 346-350].

LA - eng

KW - rate of approximation; summability of Fourier series; Lipschitz classes

UR - http://eudml.org/doc/282506

ER -

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