Uniform approximation by algebraic polynomials on the sphere of an odd-dimensional space

1987 ◽  
Vol 41 (3) ◽  
pp. 190-195
Author(s):  
A. P. Terekhin
Keyword(s):  
Uniform Approximation ◽  
Dimensional Space ◽  
Algebraic Polynomials ◽  
Approximation By Algebraic Polynomials

scholarly journals Approximation by algebraic polynomials in metric spaces $L_{\psi}$

2013 ◽  
Vol 21 ◽  
pp. 3
Author(s):  
T.A. Agoshkova
Keyword(s):  
Modulus Of Continuity ◽  
Metric Spaces ◽  
Jackson Inequality ◽  
Algebraic Polynomials ◽  
Periodic Functions ◽  
Jackson Theorem ◽  
Approximation By Algebraic Polynomials

In the space $L_{\psi}[-1;1]$ of non-periodic functions with metric $\rho(f,0)_{\psi} = \int\limits_{-1}^1 \psi(|f(x)|)dx$, where $\psi$ is a function of the type of modulus of continuity, we study Jackson inequality for modulus of continuity of $k$-th order in the case of approximation by algebraic polynomials. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function $\psi$ is not equal to zero.

On monotone and convex approximation by algebraic polynomials

1994 ◽  
Vol 46 (9) ◽  
pp. 1393-1398 ◽  
Author(s):  
K. A. Kopotun ◽  
V. V. Listopad
Keyword(s):  
Algebraic Polynomials ◽  
Convex Approximation ◽  
Approximation By Algebraic Polynomials
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