On best approximation of continuous functions

1960 ◽  
Vol 140 (2) ◽  
pp. 165-168 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Best Approximation ◽  
Continuous Functions ◽  
Approximation Of Continuous Functions

scholarly journals On the nonsymmetric approximation of continuous functions in the integral metric

2020 ◽  
Vol 27 (2) ◽  
pp. 7
Author(s):  
V.F. Babenko ◽  
O.V. Polyakov
Keyword(s):  
Best Approximation ◽  
Continuous Functions ◽  
Exact Estimate ◽  
Approximation Of Continuous Functions

In the paper, an exact estimate of the best nonsymmetric approximation in the integral metric by the constants of continuous functions that belong to the classes $H^\omega[a,b]$ is proved. Taking into account Babenko's theorem on the connection of nonsymmetric approximation with the usual best approximation in the integral metric and the best one-sided approximations, from the proved result we obtain the exact estimate for the usual best approximation obtained by N.P. Korneichuk, and the exact estimate for the best one-sided approximation obtained by V.G. Doronin and A.A. Ligun.

scholarly journals On approximation of continuous functions by piecewise-constant ones in integral metrics

1998 ◽  
Vol 6 ◽  
pp. 128
Author(s):  
O.V. Chernytska
Keyword(s):  
Upper Bound ◽  
Best Approximation ◽  
Continuous Functions ◽  
Moduli Of Continuity ◽  
Piecewise Constant ◽  
Integral Metrics ◽  
The Best Approximation ◽  
Piecewise Constant Functions ◽  
Approximation Of Continuous Functions ◽  
Decreasing Functions

We obtain upper bound of the best approximation of the classes $H^{\omega} [a, b]$ by piecewise-constant functions over uniform split in metrics of $L_{\varphi}[a, b]$ spaces, which are generated by continuous non-decreasing functions $\varphi$ that are equal to zero in zero. We study the classes of functions $\varphi$, for which the obtained bound is exact for all convex moduli of continuity.

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