Some generalized bivariate Bernstein operators
نویسندگان
چکیده
منابع مشابه
Optimality of generalized Bernstein operators
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
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We introduce and study the sequence of bivariate Generalized Bernstein operators {Bm,s}m,s, m, s ∈ N, Bm,s = I − (I − Bm) , Bim = Bm(B i−1 m ), where Bm is the bivariate Bernstein operator. These operators generalize the ones introduced and studied independently in the univariate case by Mastroianni and Occorsio [Rend. Accad. Sci. Fis. Mat. Napoli 44 (4) (1977), 151– 169] and by Micchelli [J. A...
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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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We estimate the constants sup x∈(0,1) sup f∈C[0,1]\Π1 |Bn(f,x)−f(x)| ω2 f, x(1−x) n and inf x∈(0,1) sup f∈C[0,1]\Π1 |Bn(f,x)−f(x)| ω2 f, x(1−x) n , where Bn is the Bernstein operator of degree n and ω2 is the second order modulus of continuity. 2000 Mathematical Subject Classification: 41A36, 41A10, 41A25,
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2000
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2000.14