scholarly journals Pointwise Estimates of the Hermitian Interpolation

1994 ◽  
Vol 77 (1) ◽  
pp. 31-41 ◽  
Author(s):  
I.E. Gopengauz
Keyword(s):  
Pointwise Estimates ◽  
Hermitian Interpolation

Generalized piecewise-Hermitian interpolation

1977 ◽  
Vol 28 (6) ◽  
pp. 624-629
Author(s):  
O. N. Litvin ◽  
V. V. Fed'ko
Keyword(s):  
Hermitian Interpolation

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.

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