Moduli of Monotonicity with Applications to Monotone Polynomial Approximation

1976 ◽  
Vol 7 (1) ◽  
pp. 117-130 ◽  
Author(s):  
Vasant A. Ubhaya
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.

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