Approximation Properties of Kantorovich Type Modifications of $(p, q)-$Meyer-König-Zeller Operators

Maurya, Ramapati; Sharma, Honey; Gupta, Cheeena

doi:10.33205/cma.436071

Cited by 9 publications

(5 citation statements)

References 16 publications

(15 reference statements)

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“…, , ( ; , , , ; , )|/(1 + 2 + 2 ) is bounded for sufficiently large and . Hence, we get by (25) that…”

Section: Korovkin-type Approximation Theoremsmentioning

confidence: 92%

Bivariate Chlodowsky-Stancu Variant of (p,q)-Bernstein-Schurer Operators

Vedi-Dilek¹,

Gemikonaklı²

2019

Journal of Function Spaces

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In this study, it is proposed to define bivariate Chlodowsky variant of (p,q)-Bernstein-Stancu-Schurer operators. Therefore, Korovkin-type approximation theorems and the error of approximation by using full modulus of continuity are presented. Beside this, we introduce a generalization of the bivariate Chlodowsky variant of (p,q)-Bernstein-Stancu-Schurer operators and investigate its approximation in more general weighted space. Moreover, the numerical results are discussed in order to validate the accuracy of the bivariate Chlodowsky variant of (p,q)-Bernstein-Schurer operators.

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“…, , ( ; , , , ; , )|/(1 + 2 + 2 ) is bounded for sufficiently large and . Hence, we get by (25) that…”

Section: Korovkin-type Approximation Theoremsmentioning

confidence: 92%

Bivariate Chlodowsky-Stancu Variant of (p,q)-Bernstein-Schurer Operators

Vedi-Dilek¹,

Gemikonaklı²

2019

Journal of Function Spaces

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“…Remark 4. To show the convergence of sequence of operators (6) to any continuous function defined on [0, 1], authors of [28] have discussed only some particular part of Case 2, considered in the proof of Theorem 2. They have taken condition on choosing sequences p µ and q µ satisfying 0 < q µ < p µ ≤ 1 such that lim µ→∞ p µ = 1, lim µ→∞ q µ = 1 and lim µ→∞ p µ µ = 1, lim µ→∞ q µ µ = 1, while we take more general condition on sequences p µ and q µ in above Theorem 2.…”

Section: Convergence Criteriamentioning

confidence: 99%

Lupaş post quantum Bernstein operators over arbitrary compact intervals

Khan

Iliyas

Mansoori

et al. 2021

Carpathian Math. Publ.

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This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

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“…In addition, the basic functions of a variable that can be expressed in terms of (⋅) functions can be found in the works of Yadav and Purohit [13,14]. In the last quarter of the twentieth century, the quantum calculus (also known as −calculus) can be found on the theory of approaches of operators [15,16].…”

Section: Some −Calculus: the Definitionsmentioning

confidence: 99%

“…Proof. Denoting, for convenience, the left-hand side of (31) by and using the contour integral representation (16)…”

Section: The −Generating Relationsmentioning

confidence: 99%