NOTE ON JACKSON AND BERNSTE N TYPE APPROXIMATION THEOREMS IN THE CASE OF APPROXIMATION BY ALGEBRAIC POLYNOMIALS N THE SPACES L AND C

2000 ◽  
Vol 36 (3-4) ◽  
pp. 353-358 ◽  
Author(s):  
S. Pawelke
Keyword(s):  
Periodic Function ◽  
Best Approximation ◽  
Trigonometric Polynomials ◽  
Algebraic Polynomials ◽  
Cient Condition ◽  
Approximation Theorems ◽  
Type Approximation ◽  
The Best Approximation ◽  
Approximation By Algebraic Polynomials

We con ider the best approximation E (n,f)by algebraic polynomials of degree at most n for function f in L 1 (-1, 1)or C [-1, 1]and give imple necessary and u .cient condition for E (n,f)=O (n-.),n ›.,u ing the well-known results in the ca e of ap- proximation of periodic function by trigonometric polynomials.

scholarly journals Sharp inequalities of Jackson type in weighted space $L_{2;\rho}({\mathbb{R}}^2)$

2014 ◽  
Vol 22 ◽  
pp. 17
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Best Approximation ◽  
Weighted Space ◽  
Jackson Type ◽  
Algebraic Polynomials ◽  
The Best Approximation ◽  
Differentiable Functions ◽  
Functions Of Two Variables

Sharp inequalities of Jackson type, connected with the best approximation by "angles" of algebraic polynomials have been obtained on the classes of differentiable functions of two variables in the metric of space $L_{2;\rho}({\mathbb{R}}^2)$ of the Chebyshev-Hermite weight.

scholarly journals The best approximation of classes $W^r H^{\omega}$ by algebraic polynomials in $L_1$ space

1998 ◽  
Vol 6 ◽  
pp. 52
Author(s):  
A.M. Kogan
Keyword(s):  
Asymptotic Behavior ◽  
Best Approximation ◽  
Algebraic Polynomials ◽  
The Best Approximation

We consider asymptotic behavior of the best approximation of classes $W^r H^{\omega}$ by algebraic polynomials in $L_1$ space.

scholarly journals A global optimality result using Geraghty type contraction

2014 ◽  
Vol 4 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Pranati Maity ◽  
P. Konar
Keyword(s):  
Fixed Point ◽  
Best Approximation ◽  
Approximate Solutions ◽  
Global Optimality ◽  
Approximation Theorems ◽  
The Best Approximation ◽  
Optimal Values ◽  
Type Contraction

In this paper we prove two proximity point results for finding the distance between two sets. Unlike the best approximation theorems they provide with globally optimal values. Here our approach is to reduce the problem to that of finding optimal approximate solutions of some fixed point equations. We use Geraghty type contractive inequalities in our theorem. Two illustrative examples are given.

Sign in / Sign up

Export Citation Format

Share Document