1985
DOI: 10.1016/0021-9045(85)90089-9
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Monotone approximation with linear differential operators

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Cited by 31 publications
(13 citation statements)
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“…In [2] we proved the following Theorem 4. Let h, v, r be integers, 0 ≤ h ≤ v ≤ r and let f P C r pIq, with f prq having modulus of smoothness ω s`f prq , δ˘there, s ≥ 1.…”
Section: Theorem 2 Implies the Usefulmentioning
confidence: 85%
See 1 more Smart Citation
“…In [2] we proved the following Theorem 4. Let h, v, r be integers, 0 ≤ h ≤ v ≤ r and let f P C r pIq, with f prq having modulus of smoothness ω s`f prq , δ˘there, s ≥ 1.…”
Section: Theorem 2 Implies the Usefulmentioning
confidence: 85%
“…In [3] the authors replaced the kth derivative with a linear differential operator of order k. We mention this motivating result. Theorem 1.…”
Section: Introductionmentioning
confidence: 99%
“…Date: February 14, 2018. 1 Furthermore, if there also exists a compact subinterval J(∋ 0) of R, and C 2 > 0 such that…”
Section: Introductionmentioning
confidence: 99%
“…There the problem was: given a positive integer r, approximate with rates a given function whose rth derivative is > 0 by polynomials having the same property. This initial problem was generalized by G. A. Anastassiou and O. Shisha in 1985 (see [1]) by replacing the rth derivative with a linear differential operator of order r. The rate of the related uniform convergence was given through the first modulus of continuity.…”
Section: Introductionmentioning
confidence: 99%