Negative result in pointwise 3-convex polynomial approximation
Let $Δ^3$ be the set of functions three times continuously differentiable on $[−1, 1]$ and such that $f'''(x) ≥ 0,\; x ∈ [−1, 1]$. We prove that, for any $n ∈ ℕ$ and $r ≥ 5$, there exists a function $f ∈ C^r [−1, 1] ⋂ Δ^3 [−1, 1]$ such that $∥f (r)∥_{C[−1, 1]} ≤ 1$ and, fo...
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| Date: | 2009 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2009
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3040 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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