Approximation of periodic functions in Orlicz spaces

Linear methods of summing Fourier series and approximation in weighted Orliczspaces

“…The problems of approximation theory in weighted and nonweighted Lebesgue spaces, as well as weighted and nonweighted Orlicz spaces were investigated by several authors (see, for example, [3][4][5][7][8][9][10][11][12][13][14][15]17,18,22,23,[26][27][28][30][31][32][33][34]).…”

“…In the present paper, we estimate the norms of R n (f, λ) and R r (f, λ) in the weighted Orlicz spaces L M (T, ω). Similar problems in different spaces were investigated in [3,5,15,18,27,30,[32][33][34].…”

Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces

“…The problems of approximation theory in weighted and nonweighted Lebesgue spaces, weighted and nonweighted Orlicz spaces have been investigated by several authors (see, e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][30][31][32]36,37,45,46]). …”

Approximation of periodic functions in weighted Orlicz spaces

“…In the theory of approximation, statements of this sort are called direct theorems. In this paper we investigate some direct theorems of approximation theory in the weighted Orlicz spaces and get a generalization of the results appeared in [17].…”

“…Approximation by trigonometric polynomials and other related problems in the Orlicz and weighted Orlicz spaces were studied in [2,[8][9][10][11][12]17,18,21,23,24].…”