scholarly journals On the Degree of Approximation of Continuous Functions by Means of Fourier Series in the Holder Metric

2019 ◽  
Vol 35 (4) ◽  
pp. 392-404
Author(s):  
global sci
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Hölder Metric ◽  
Approximation Of Continuous Functions

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.

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 Degree of Approximation of Functionsf~∈HωClass by the(Np·E1)Means in the Hölder Metric

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Kejal Khatri
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Hölder Metric ◽  
Approximation Of A Function

A new estimate for the degree of approximation of a functionf˜∈Hωclass by(Np·E1)means of its Fourier series has been determined. Here, we extend the results of Singh and Mahajan (2008) which in turn generalize the result of Lal and Yadav (2001). Some corollaries have also been deduced from our main theorem.

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