scholarly journals Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like $$\vert x\vert ^{{\alpha }+i{\beta }}$$

2021 ◽  
Author(s):  
Michael I. Ganzburg
Keyword(s):  
Asymptotic Behaviour ◽  
Polynomial Approximation ◽  
Approximation Of Functions ◽  
Polynomial Approximation Of Functions

scholarly journals On uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums

2021 ◽  
Vol 16 ◽  
pp. 41
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk ◽  
V.I. Zabutna
Keyword(s):  
Finite Number ◽  
Polynomial Approximation ◽  
Analytic Functions ◽  
Function Theory ◽  
Approximation Of Functions ◽  
Constructive Function ◽  
Asymptotic Values ◽  
Uniform Polynomial Approximation ◽  
Polynomial Approximation Of Functions

We show that some of results, obtained by S.N. Bernstein, on constructive function theory, under certain conditions, take place for uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums. On the base of obtained results for certain class of analytic functions we calculate asymptotic values of some $n$-widths.

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