On the best approximations and Kolmogorov widths of besov classes of periodic functions of many variables

1995 ◽  
Vol 47 (1) ◽  
pp. 91-106 ◽  
Author(s):  
A. S. Romanyuk
Keyword(s):  
Periodic Functions ◽  
Best Approximations ◽  
Kolmogorov Widths

On Jackson Type Inequalities for the Best Approximations of Periodic Functions

2015 ◽  
Vol 210 (5) ◽  
pp. 654-663
Author(s):  
V. V. Zhuk
Keyword(s):  
Jackson Type ◽  
Periodic Functions ◽  
Best Approximations

scholarly journals Approximation of functions and their conjugates in Lp and uniform metric by Euler means

2018 ◽  
Vol 51 (1) ◽  
pp. 141-150
Author(s):  
Sergey S. Volosivets ◽  
Anna A. Tyuleneva
Keyword(s):  
Uniform Approximation ◽  
Conjugate Functions ◽  
Periodic Functions ◽  
Best Approximations ◽  
Approximation Of Functions

Abstract For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.

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