scholarly journals Pointwise estimates for monotone polynomial approximation

1985 ◽  
Vol 1 (1) ◽  
pp. 323-331 ◽  
Author(s):  
Ronald A. DeVore ◽  
Xiang Ming Yu
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates ◽  
Monotone Polynomial Approximation

scholarly journals Interpolatory pointwise estimates for monotone polynomial approximation

2018 ◽  
Vol 459 (2) ◽  
pp. 1260-1295 ◽  
Author(s):  
K.A. Kopotun ◽  
D. Leviatan ◽  
I.A. Shevchuk
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates ◽  
Monotone Polynomial Approximation

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals Pointwise estimates for convex polynomial approximation

1986 ◽  
Vol 98 (3) ◽  
pp. 471-471 ◽  
Author(s):  
D. Leviatan
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates

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.

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

scholarly journals Interpolatory pointwise estimates for convex polynomial approximation

2020 ◽  
Author(s):  
K. A. Kopotun ◽  
D. Leviatan ◽  
I. L. Petrova ◽  
I. A. Shevchuk
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates

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

scholarly journals Monotone polynomial approximation in $L^p$

1989 ◽  
Vol 19 (1) ◽  
pp. 231-242
Author(s):  
D. Leviatan
Keyword(s):  
Polynomial Approximation ◽  
Monotone Polynomial Approximation

Monotone polynomial approximation inL p space

1987 ◽  
Vol 3 (4) ◽  
pp. 315-326 ◽  
Author(s):  
Yu Xiangming
Keyword(s):  
Polynomial Approximation ◽  
Monotone Polynomial Approximation

Exact order of pointwise estimates for polynomial approximation with Hermite interpolation

2021 ◽  
Vol 264 ◽  
pp. 105538
Author(s):  
K.A. Kopotun ◽  
D. Leviatan ◽  
I.A. Shevchuk
Keyword(s):  
Polynomial Approximation ◽  
Hermite Interpolation ◽  
Exact Order ◽  
Pointwise Estimates
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