Moduli of Monotonicity with Applications to Monotone Polynomial Approximation

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

2016 ◽  
Vol 68 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Kirill Kopotun ◽  
Dany Leviatan ◽  
Igor Shevchuk

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.



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






2018 ◽  
Vol 459 (2) ◽  
pp. 1260-1295 ◽  
Author(s):  
K.A. Kopotun ◽  
D. Leviatan ◽  
I.A. Shevchuk


1985 ◽  
Vol 1 (1) ◽  
pp. 323-331 ◽  
Author(s):  
Ronald A. DeVore ◽  
Xiang Ming Yu


1972 ◽  
Vol 172 ◽  
pp. 465-465 ◽  
Author(s):  
D. J. Newman ◽  
Eli Passow ◽  
Louis Raymon




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