Approximation of Functions by Generalized Parametric Blending-Type Bernstein Operators

Aktuğlu, Hüseyin; Zaheriani, Seyed Yashar

doi:10.1007/s40995-020-00957-6

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…Recently, shape parameters α and λ were used to extend Bernstein operators to α-Bernstein type (see [5,6,8,[11][12][13][14][15][16][17][18]) and λ-Bernstein type operators (see [9,[19][20][21][22][23][24][25][26]) in order to approximate functions better, respectively. The convergence of linear positive operators by the shape parameters α and λ in the space of continuous functions of two variables was studied in [27][28][29] and [22,30,31], respectively.…”

Section: Introductionmentioning

confidence: 99%

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

et al. 2022

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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. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A-statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters α and λ, and they propose better approximation results.

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Section: Introductionmentioning

confidence: 99%

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

et al. 2022

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Generalized blending type Bernstein operators based on the shape parameter λ

et al. 2022

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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 type α-Bernstein and λ-Bernstein operators as special case. In this paper, we prove some approximation theorems for these operators. Approximation properties of our operators are illustrated on graphs for variables s, α, λ, and n. It should be mentioned that our operators for $\lambda =1$ λ = 1 have better approximation than Bernstein and α-Bernstein operators.

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Some approximation properties of the parametric generalization of Bleimann-Butzer-Hahn operators

Dalmanoğlu

2023

Filomat

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The present paper deals with a new generalization of Bleimann-Butzer-Hahn operators that depends on a real non-negative parameter ? and is therefore called the ?-Bleimann-Butzer-Hahn operators. We examined the uniform convergence of the newly defined operators with the help of the Korovkin type approximation theorem. The rate of convergence is investigated by means of the modulus of continuity and by Lipschitz type maximal functions. A Voronovskaya type theorem is also obtained and lastly graphical examples are given in order to illustrate the convergence of the operators to the given functions.

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Approximation of Functions by Generalized Parametric Blending-Type Bernstein Operators

Cited by 4 publications

References 33 publications

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

Generalized blending type Bernstein operators based on the shape parameter λ

Some approximation properties of the parametric generalization of Bleimann-Butzer-Hahn operators

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