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

Volume 95 / 2011

Włodzimierz Łenski, Bogdan Szal Banach Center Publications 95 (2011), 339-351 MSC: 42A24. DOI: 10.4064/bc95-0-20

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].

Authors

  • Włodzimierz ŁenskiUniversity of Zielona Góra
    Faculty of Mathematics
    Computer Science and Econometrics
    ul. Prof. Szafrana 4a
    65-516 Zielona Góra, Poland
    e-mail
  • Bogdan SzalUniversity of Zielona Góra
    Faculty of Mathematics
    Computer Science and Econometrics
    ul. Prof. Szafrana 4a
    65-516 Zielona Góra, Poland
    e-mail

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