The order of approximation of continuous functions by certain linear means of their Fourier series

1971 ◽  
Vol 9 (6) ◽  
pp. 358-364
Author(s):  
V. A. Baskakov
Keyword(s):  
Fourier Series ◽  
Continuous Functions ◽  
Order Of Approximation ◽  
Linear Means ◽  
Approximation Of Continuous Functions

scholarly journals The approximation of continuous functions by Riesz typical means of their Fourier series

1967 ◽  
Vol 7 (4) ◽  
pp. 539-544 ◽  
Author(s):  
B. Kwee
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Continuous Functions ◽  
Positive Order ◽  
Approximation Of Continuous Functions

Let (x) be a continuous function with period 2π. It is well known that the Fourier series of (x) is summable Riesz of any positive order to (x). The aim of this paper is the proof of the following theorem.

scholarly journals A Note on the Approximation of Continuous Functions by Riesz Typical Means of Their Fourier Series

1969 ◽  
Vol 9 (1-2) ◽  
pp. 180-181 ◽  
Author(s):  
B. Kwee
Keyword(s):  
Fourier Series ◽  
Positive Integer ◽  
Continuous Functions ◽  
Image Position ◽  
Approximation Of Continuous Functions

In [1], the following theorem is proved:THEOREM. If f ∈C2π, α is a positive integer, and then Where , .

scholarly journals On the degree of approximation of continuous functions by a specific transform of partial sums of their Fourier series

2021 ◽  
Vol 25 (1) ◽  
pp. 5-19
Author(s):  
Xhevat Krasniqi
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Bounded Variation ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Auxiliary Function ◽  
Partial Sums ◽  
The Mean ◽  
Approximation Of Continuous Functions ◽  
Positive Integers

Using the Mean Rest Bounded Variation Sequences or the Mean Head Bounded Variation Sequences, we have proved four theorems pertaining to the degree of approximation in sup-norm of a continuous function f by general means τλn;A(f) of partial sums of its Fourier series. The degree of approximation is expressed via an auxiliary function H(t) ≥ 0 and via entries of a matrix whose indices form a strictly increasing sequence of positive integers λ := {λ(n)}∞n=1.

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