REFERENCES
A. Zygmund, “The approximation of functions by typical means of their Fourier series,” Duke Math. J., 12 (1945), no. 4, 695-704.
A. F. Timan, Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow, 1960.
V. V. Zhuk, Approximation of Periodic Functions [in Russian], Leningrad State Univ., Leningrad, 1982.
N. A. Il′yasov, “Approximation of periodic functions by the Zygmund means,” Mat. Zametki [Math. Notes], 39 (1986), no. 3, 367-382.
N. A. Il′yasov, “Approximation of periodic functions by the Fejér-Zygmund means in different metrics,” Mat. Zametki [Math. Notes], 48 (1990), no. 4, 48-57.
N. A. Il′yasov, “The inverse theorem of approximation theory in different metrics,” Mat. Zametki [Math. Notes], 50 (1991), no. 6, 57-65.
N. A. Il′yasov, “Approximation by the Fejér-Zygmund means on certain classes of periodic functions in Lp,” Trudy Azerbaijan. Mat. Obshch., 2 (1996), 91-110.
A. A. Konyushkov, “Best approximations by trigonometric polynomials and the Fourier coefficients,” Mat. Sb. [Math. USSR-Sb.], 44 (1958), no. 1, 53-84.
S. B. Stechkin, “On the order of best approximations of continuous functions,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 15 (1951), no. 3, 219-242.
S. B. Stechkin, “Approximation of periodic functions by the Fejér sums,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 62 (1961), 48-60.
M. F. Timan, “Certain linear processes of summation of Fourier series and best approximations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 145 (1962), no. 4, 741-743.
M. F. Timan, “Best approximations of a function and linear methods of summation of Fourier series,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 29 (1965), no. 3, 587-604.
R. M. Trigub, “Constructive characteristics of certain classes of functions,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 29 (1965), no. 3, 615-630.
V. V. Zhuk, “On the approximation of a 2π-periodic function by the linear operator,” Sbornik Nauchn. Trudov Leningrad. Mech. Institut. (1965), no. 50, 93-115.
N. A. Il′yasov, “On the inverse theorem of approximation theory of periodic functions in different metrics,” Mat. Zametki [Math. Notes], 52 (1992), no. 2, 53-61.
V. É. Geit, “On the accuracy of some inequalities in approximation theory,” Mat. Zametki [Math. Notes], 10 (1971), no. 5, 571-582.
V. E. Geit, “On the structural and constructive properties of a function and its conjugate in L,” Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], (1972), no. 7, 19-30.
V. É. Geit, “Embedding theorems for some classes of periodic continuous functions,” Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], (1972), no. 4, 67-77.
V. I. Kolyada, “Embedding theorems and inequalities of different metrics for best approximations,” Mat. Sb. [Math. USSR-Sb.] 102 (1977), no. 195-215.
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On the Order of Approximation in the Uniform Metric by the Fejér--Zygmund Means on the Classes E p[ɛ]. Mathematical Notes 69, 625–633 (2001). https://doi.org/10.1023/A:1017372708394
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DOI: https://doi.org/10.1023/A:1017372708394