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Approximation of functions from L p ( ω ) β by general linear operators of their Fourier series

Włodzimierz ŁenskiBogdan Szal — 2011

Banach Center Publications

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....

Approximation of functions from L p ( ω ) β by linear operators of their Fourier series

Włodzimierz ŁenskiBogdan Szal — 2011

Commentationes Mathematicae

We show the results corresponding to theorems of S. Lal [Appl. Math. Comput., 209 (2009) 346-350] on the rate of approximation of functions from the generalized integral Lipschitz classes by matrix summability means of their Fourier series as well as to the authors theorems [Acta Comment. Univ. Tartu. Math., 13 (2009), 11-24] also on such approximations.

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