On monotone and doubly monotone polynomial approximation

1992 ◽  
Vol 59 (3-4) ◽  
pp. 395-399 ◽  
Author(s):  
S. G. Gal ◽  
J. Szabados
Keyword(s):  
Polynomial Approximation ◽  
Monotone Polynomial Approximation

Constrained Approximation with Jacobi Weights

2016 ◽  
Vol 68 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Kirill Kopotun ◽  
Dany Leviatan ◽  
Igor Shevchuk
Keyword(s):  
Polynomial Approximation ◽  
Spline Approximation ◽  
Modulus Of Smoothness ◽  
Jacobi Weights ◽  
Jacobi Weight ◽  
Constrained Approximation ◽  
Monotone Polynomial Approximation

AbstractIn this paper, we prove that for ℓ = 1 or 2 the rate of best ℓ- monotone polynomial approximation in the Lp norm (1 ≤ p ≤) weighted by the Jacobi weight with , is bounded by an appropriate (ℓ + 1)-st modulus of smoothness with the same weight, and that this rate cannot be bounded by the (ℓ + 2)-nd modulus. Related results on constrained weighted spline approximation and applications of our estimates are also given.

Sign in / Sign up

Export Citation Format

Share Document