General linear summation of the Vilenkin-Fourier series

1985 ◽  
Vol 46 (3-4) ◽  
pp. 285-295 ◽  
Author(s):  
He Zelin
Keyword(s):  
Fourier Series ◽  
General Linear ◽  
Linear Summation

On linear summation methods of Fourier series

1979 ◽  
Vol 5 (2) ◽  
pp. 119-133 ◽  
Author(s):  
Я. С. Бугров
Keyword(s):  
Fourier Series ◽  
Linear Summation ◽  
Summation Methods

scholarly journals Approximation of Conjugate Functions by General Linear Operators of Their Fourier Series at the Lebesgue Points

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Włodzimierz Łenski ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Linear Operators ◽  
General Linear ◽  
Conjugate Functions ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Lebesgue Points ◽  
Norm Approximation

AbstractThe pointwise estimates of the deviations r T͂n,A,Bf (·) - f͂͂ (·) and T͂n,A,Bf (·) - f͂͂ (·,ε) in terms of moduli of continuity ω̃f and r ω̃f are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal [3, Theorem 1, p. 437].

Some linear summation methods for Fourier series

1998 ◽  
Vol 189 (5) ◽  
pp. 771-795
Author(s):  
A A Talalyan ◽  
G G Gevorkyan ◽  
G A Karagulyan
Keyword(s):  
Fourier Series ◽  
Linear Summation ◽  
Summation Methods

scholarly journals Approximation of functions by linear summation methods in the Orlicz type spaces

2020 ◽  
Vol 17 (2) ◽  
pp. 152-170
Author(s):  
Stanislav Chaichenko ◽  
Viktor Savchuk ◽  
Andrii Shidlich
Keyword(s):  
Fourier Series ◽  
Moduli Of Smoothness ◽  
Approximation Of Functions ◽  
Linear Summation ◽  
Summation Methods ◽  
Type Spaces

Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces S_M. In particular, in terms of approximations by such methods, constructive characteristics are obtained for classes of functions whose moduli of smoothness do not exceed a certain majorant.

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