Estimates for the best approximation and integral modulus of continuity of a function in terms of its Fourier coefficients

1998 ◽  
Vol 50 (4) ◽  
pp. 562-571
Author(s):  
P. V. Zaderei ◽  
B. A. Smal’
Keyword(s):  
Modulus Of Continuity ◽  
Best Approximation ◽  
Fourier Coefficients ◽  
Integral Modulus ◽  
The Best Approximation

scholarly journals On approximation by trigonometrical polynomials in $L_2$ space

2016 ◽  
Vol 24 ◽  
pp. 89
Author(s):  
O.V. Polyakov
Keyword(s):  
Modulus Of Continuity ◽  
Best Approximation ◽  
Generalized Modulus Of Continuity ◽  
Jackson Type ◽  
The Best Approximation ◽  
Differentiable Functions

We obtain certain inequalities of Jackson type, connecting the value of the best approximation of periodic differentiable functions and the generalized modulus of continuity of the highest derivative.

Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces

2006 ◽  
Vol 13 (2) ◽  
pp. 315-332
Author(s):  
István Mező
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Lebesgue Space ◽  
Best Approximation ◽  
Acta Math ◽  
Function Spaces ◽  
Vilenkin Group ◽  
Strong Connection ◽  
The Best Approximation

Abstract We rephrase Fridli's result [Fridli, Acta Math. Hungar. 45: 393–396, 1985] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [Gát, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 17: 161–169, 2001] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.

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