A survey on the Weierstrass approximation theorem.

Pérez, Dilcia; Quintana, Yamilet

Displaying similar documents to “A survey on the Weierstrass approximation theorem.”

A note on lacunary approximation on [-1,1]

S. Zhou (1993)

Colloquium Mathematicae

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A survey of weighted polynomial approximation with exponential weights.

Lubinsky, Doron (2007)

Surveys in Approximation Theory (SAT)[electronic only]

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A counterexample in comonotone approximation in $L^{p}$ space

Xiang Wu, Song Zhou (1993)

Colloquium Mathematicae

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Refining the idea used in [24] and employing very careful computation, the present paper shows that for 0 < p ≤ ∞ and k ≥ 1, there exists a function $f \in C_{[- 1, 1]}^{k}$ , with $f^{(k)} (x) \geq 0$ for x ∈ [0,1] and $f^{(k)} (x) \leq 0$ for x ∈ [-1,0], such that lim supn→∞ (en(k)(f)p) / (ωk+2+[1/p](f,n-1)p) = + ∞ where $e_{n}^{(k)} {(f)}_{p}$ is the best approximation of degree n to f in $L^{p}$ by polynomials which are comonotone with f, that is, polynomials P so that $P^{(k)} (x) f^{(k)} (x) \geq 0$ for all x ∈ [-1,1]. This theorem, which is a particular case of a more general one, gives a complete...

On some properties of the Picard operators

Lucyna Rempulska, Karolina Tomczak (2009)

Archivum Mathematicum

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We consider the Picard operators $𝒫_{n}$ and $𝒫_{n; r}$ in exponential weighted spaces. We give some elementary and approximation properties of these operators.