Parametric generalization of the Meyer-König-Zeller operators

Sofyalıoğlu, Melek; Kanat, Kadir; Çekіm, Bayram

doi:10.1016/j.chaos.2021.111417

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…The convergence of the generalized Bernstein operator Q n,λ ( f ; y) given in Equation ( 13) is demonstrated in this section using the same functions examined in [26]. Taking…”

Section: Graphical Analysismentioning

confidence: 92%

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

Ong

Yap

et al. 2022

Axioms

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The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney–Sharma operator is the Szász–Mirakyan operator averaged by a certain probability distribution.

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“…The convergence of the generalized Bernstein operator Q n,λ ( f ; y) given in Equation ( 13) is demonstrated in this section using the same functions examined in [26]. Taking…”

Section: Graphical Analysismentioning

confidence: 92%

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

Ong

Yap

et al. 2022

Axioms

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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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“…Then, a number of interesting generalizations about q-calculus were studied by Jackson (1910), Koelink & Koornwinder (1990), Phillips (1997), Kac & Cheung (2002), De Sole & Kac (2005), Doğru & Gupta (2005, 2006, Gupta & Heping (2008), Gupta & Aral (2010), Gupta & Karsli (2012), Aral et al (2013), Yüksel (2013). Sahai & Yadav (2007), Kanat & Sofyalıoğlu (2018), Sofyalıoğlu et al (2021) introduced the generalization of (𝑝, 𝑞) −calculus. Recently, the series of studies on (𝑝, 𝑞)-generalizations with a sequence of linear positive operators have been made by Mursaleen et al (2015 a,b,c), Acar et al (2016Acar et al ( , 2018, Gupta (2018), Cai et al (2021), .…”

Section: Introductionmentioning

confidence: 99%

Investigating (p,q)-hybrid Durrmeyer-type Operators in terms of Their Approximation Properties

Kantar

Yüksel

2022

Gazi University Journal of Science Part A: Engineering and Innovation

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This study introduces (𝑝, 𝑞)-hybrid Durrmeyer-Stancu type linear positive operators, which are generalized forms of 𝑞-hybrid Durrmeyer-Stancu-type linear positive operators and examines their approximation properties. The first modulus of continuity on a finite interval is introduced using Peetre's K-functional. Then, the weighted approximation theorem in a weighted space is provided using Gadzhiev's weighted Korovkin-type theorem. Finally, these operators' rates of convergence are obtained for the continuous functions. CiteDinlemez Kantar, U., & Yuksel, I. (2022). Investigating (p,q)-hybrid Durrmeyer-type operators in terms of their approximation properties.

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Parametric generalization of the Meyer-König-Zeller operators

Cited by 9 publications

References 14 publications

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

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

Investigating (p,q)-hybrid Durrmeyer-type Operators in terms of Their Approximation Properties

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