Optimal approximation class for multivariate Bernstein operators
نویسندگان
چکیده
منابع مشابه
Multivariate Bernstein operators and redundant systems
The Bernstein operator Bn for a simplex in Rd is naturally defined via the Bernstein basis obtained from the barycentric coordinates given by its vertices. Here we consider a generalisation of this basis and the Bernstein operator, which is obtained from generalised barycentric coordinates that are given for more general configurations of points in Rd . We call the associated polynomials a Bern...
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for n ≥ α, where α, β are integers satisfying α ≥ β ≥ 0 and In ⊆ {0,1,2, . . . ,n} is a certain index set. For α = β = 0, In = {0}, this definition reduces to the BernsteinDurrmeyer operators, which were first studied by Derriennic [3]. Also if α = β = 1, In = {0}, we obtain the recently introduced sequence of Gupta and Maheshwari [4], that is, Mn,1,1(f ,x)≡ Pn(f ,x) which is defined as Pn(f ,x...
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*Correspondence: [email protected] College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People’s Republic of China Abstract We give the direct and inverse approximation theorems for a new type of Bernstein-Durrmeyer operators with the mod...
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In this paper we construct new operators of Bernstein type with a better approximation than the classical Bernstein operator for some classes of functions on the whole interval [0,1]. Convergence of these operators and their shape preserving properties are discussed. We determine the subintervals in [0,1] in which the approximation order of constructed operators is better than that of the Berns...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1993
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1993.158.93