Direct and Inverse Estimates for Bernstein Polynomials

Felten, Michael

doi:10.1007/s003659900084

Cited by 33 publications

(17 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, with respect to Theorem 1, this term can also be taken as | ( f, |A(v&x)(x)|Â (x)) for other choices of admissible step-weight functions of the Ditzian Totik modulus. In the case of Bernstein-type operators it will be seen that the error bound (10) can be improved by suitable choices of .…”

Section: Direct Resultsmentioning

confidence: 97%

Local and Global Approximation Theorems for Positive Linear Operators

Felten

1998

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

Section: Direct Resultsmentioning

confidence: 97%

Local and Global Approximation Theorems for Positive Linear Operators

Felten

1998

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

“…holds true for all n ∈ N. Other direct pointwise estimates in terms of K ϕ are proved in [6]. We point out that neither from [6] nor from [4] is it possible to deliver (3.1) as a straightforward corollary.…”

Section: Upper and Lower Pointwise Boundsmentioning

confidence: 91%

“…We point out that neither from [6] nor from [4] is it possible to deliver (3.1) as a straightforward corollary.…”

Section: Upper and Lower Pointwise Boundsmentioning

confidence: 92%

Pointwise Approximation by Bernstein Polynomials

Tachev¹

2012

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

We improve the degree of pointwise approximation of continuous functions f (x) by Bernstein operators, when x is close to the endpoints of [0,1]. We apply the new estimate to establish upper and lower pointwise estimates for the test function g(x) = x log(x) + (1 − x) log(1 − x). At the end we prove a general statement for pointwise approximation by Bernstein operators.2010 Mathematics subject classification: primary 41A10; secondary 41A15, 41A25, 41A36.

show abstract

“…First we consider those values of x for which ϕ 2 (x) ≥ 1 6n . Due to the concavity of the function ϕ 2λ (x) (see, e.g., Felten [4]) it is easy to verify that…”

Section: Definition 21mentioning

confidence: 99%

“…This technique was used, for example, by Ditzian in [2] and further developed by Felten (see [4,5]). Details will be given in the next section.…”

Section: Introductionmentioning

confidence: 99%