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

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 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

scholarly journals Pointwise estimates for polynomial approximation on the semiaxis

2010 ◽  
Vol 162 (11) ◽  
pp. 2078-2105 ◽  
Author(s):  
Giuseppe Mastroianni ◽  
Woula Themistoclakis
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates

Interpolatory Pointwise Estimates for Polynomial Approximation

2000 ◽  
Vol 16 (4) ◽  
pp. 603-629 ◽  
Author(s):  
H. H. Gonska ◽  
D. Leviatan ◽  
I. A. Shevchuk ◽  
H. -J. Wenz
Keyword(s):  
Polynomial Approximation ◽  
Pointwise Estimates
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