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Approximation properties of λ-Bernstein operators [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we introduce a new type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$, we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz ...
Qing-Bo Cai, Bo-Yong Lian, Guorong Zhou
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Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we introduce a family of GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of ...
Qing-Bo Cai, Guorong Zhou
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The Bézier variant of Kantorovich type λ-Bernstein operators [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$. We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation ...
Qing-Bo Cai
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Approximation properties of λ-Kantorovich operators [PDF]
Journal of Inequalities and Applications, 2018 In the present paper, we study a new type of Bernstein operators depending on the parameter λ∈[−1,1] $\lambda\in[-1,1]$. The Kantorovich modification of these sequences of linear positive operators will be considered.
Ana-Maria Acu +2 more
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Generalized blending type Bernstein operators based on the shape parameter λ
Journal of Inequalities and Applications, 2022 In the present paper, we construct a new class of operators based on new type Bézier bases with a shape parameter λ and positive parameter s. Our operators include some well-known operators, such as classical Bernstein, α-Bernstein, generalized blending ...
Halil Gezer +3 more
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On the shape-preserving properties of λ-Bernstein operators
Journal of Inequalities and Applications, 2022 We investigate the shape-preserving properties of λ-Bernstein operators B n , λ ( f ; x ) $B_{n,\lambda } ( f;x ) $ that were recently introduced Bernstein-type operators defined by a new Beziér basis with shape parameter λ ∈ [ − 1 , 1 ] $\lambda \in ...
Lian-Ta Su, Gökhan Mutlu, Bayram Çekim
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Chlodowsky type $\left( \lambda,q\right)$-Bernstein Stancu operators of Pascal rough triple sequences [PDF]
Journal of Mahani Mathematical Research, 2023 The fundamental concept of statistical convergence first was put forward by Steinhaus and at the same time but also by Fast \cite{Fast} independently both for complex and real sequences. In fact, the convergence in terms of statistical manner can be
Ayhan Esi +2 more
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Mathematics, 2022 An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations ...
Faruk Özger +2 more
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Mathematics, 2022 This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer.
Qing-Bo Cai +3 more
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On the Durrmeyer variant of q-Bernstein operators based on the shape parameter λ
Journal of Inequalities and Applications, 2023 In this work, we consider several approximation properties of a Durrmeyer variant of q-Bernstein operators based on Bézier basis with the shape parameter λ ∈ [ − 1 , 1 ] $\lambda \in[ -1,1]$ .
Lian-Ta Su +3 more
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