Some approximation results for Stancu type Lupaş–Schurer operators based on ( p, q )-integers

Kanat, Kadir; Sofyalıoğlu, Melek

doi:10.1016/j.amc.2017.08.046

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…converge to continuous function f (u) uniformly in [0, 1] for each real γ, δ such that 0 ≤ γ ≤ δ. For more recent literatures on Stancu type operators on can see [1,4,7,[15][16][17][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators

QASIM¹,

MURSALEEN²,

KHAN³

et al. 2022

KgJMat

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The purpose of this paper is to introduce Stancu variant of generalized Lupaş operators whose construction depends on a continuously diﬀerentiable, increasing and unbounded function ρ. Depending on the selection of γ and δ, these operators are more ﬂexible than the generalized Lupaş operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

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Section: Introductionmentioning

confidence: 99%

On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators

QASIM¹,

MURSALEEN²,

KHAN³

et al. 2022

KgJMat

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“…Due to its comprehensive applications, the approximation behaviors of linear positive operators in ( , ) pq -calculus have been studied actively by different authors [5][6][7][8][9][10]. Most recently, Aral and Gupta [11] have initiated the ( , ) pq -analogue of the Baskakov operators.…”

Section: Introductionmentioning

confidence: 99%

Approximation Properties of Stancu-Type (p,q)-Baskakov Operators

Kanat¹,

Sofyalıoğlu²

2019

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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This paper deals with the construction of the Stancu type modification of the Baskakov operators by using (,) pq-integers. The rate of convergence of these operators are obtained by using Peetre's K-functional and modulus of continuity. In addition, the pointwise estimation of the newly constructed operators are examined for functions belong to a Lipschitz space. Finally, the convergence of the constructed operators to some functions is shown with the help of MATLAB.

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“…In the -calculus, parameter p provides suppleness to the approximation. Some recent articles are [ 1 , 4 – 6 , 9 , 10 , 13 ], and [ 21 ]. Motivated by the work of Khalid et al [ 15 ], now we define a Kantorovich type Lupaş-Schurer operators based on the -calculus.…”

Section: Introductionmentioning

confidence: 99%

Approximation by ( p , q ) $(p,q)$ -Lupaş–Schurer–Kantorovich operators

Kanat

Sofyalıoğlu

2018

J Inequal Appl

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In the current paper, we examine the -analogue of Kantorovich type Lupaş–Schurer operators with the help of -Jackson integral. Then, we estimate the rate of convergence for the constructed operators by using the modulus of continuity in terms of a Lipschitz class function and by means of Peetre’s K-functionals based on Korovkin theorem. Moreover, we illustrate the approximation of the -Lupaş–Schurer–Kantorovich operators to appointed functions by the help of Matlab algorithm and then show the comparison of the convergence of these operators with Lupaş–Schurer operators based on -integers.

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Some approximation results for Stancu type Lupaş–Schurer operators based on ( p, q )-integers

Cited by 9 publications

References 9 publications

On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators

On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators

Approximation Properties of Stancu-Type (p,q)-Baskakov Operators

Approximation by ( p , q ) $(p,q)$ -Lupaş–Schurer–Kantorovich operators

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