scholarly journals Some Remarks on Equivalence of Moduli of Smoothness

2001 ◽  
Vol 113 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Guanzhen Zhou ◽  
Songping Zhou
Keyword(s):  
Moduli Of Smoothness

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.

Estimates of Functions with Transformed Double Fourier Series

2021 ◽  
Vol 58 (1) ◽  
pp. 32-83
Author(s):  
Boris V. Simonov
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Moduli Of Smoothness ◽  
Best Approximations

The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.

scholarly journals Univariate splines: Equivalence of moduli of smoothness and applications

2006 ◽  
Vol 76 (258) ◽  
pp. 931-945 ◽  
Author(s):  
Kirill A. Kopotun
Keyword(s):  
Moduli Of Smoothness

Berry–Esseen Bounds for Standardized Subordinators via Moduli of Smoothness

2007 ◽  
Vol 20 (2) ◽  
pp. 221-235 ◽  
Author(s):  
José Antonio Adell ◽  
Alberto Lekuona
Keyword(s):  
Moduli Of Smoothness
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