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.

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

2020 ◽  
Vol 249 (5) ◽  
pp. 705-719
Author(s):  
Stanislav Chaichenko ◽  
Viktor Savchuk ◽  
Andrii Shidlich
Keyword(s):  
Approximation Of Functions ◽  
Linear Summation ◽  
Summation Methods ◽  
Type Spaces

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

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 Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

2019 ◽  
Vol 69 (6) ◽  
pp. 1367-1380 ◽  
Author(s):  
Stanislav Chaichenko ◽  
Andrii Shidlich ◽  
Fahreddin Abdullayev
Keyword(s):  
Fractional Order ◽  
Moduli Of Smoothness ◽  
Best Approximations ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

Sign in / Sign up

Export Citation Format

Share Document