Generalized Lupaş operators

İlarslan, Hatice Gül İnce; Aral, Ali; Başcanbaz‐Tunca, Gülen

doi:10.1063/1.5020468

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Remark 1. We observe from Lemma 1 and Corollary 1, that for q = 1, we get the moments and central moments of generalized Lupaş operators [7].…”

Section: Proof By Taking Into Account the Recurrence Relationmentioning

confidence: 84%

“…Very recently motivated by the above work,İlarslan et al [7] introduced a new modification of Lupaş operators [8] using a suitable function ρ, which satisfies the following properties:…”

Section: Introductionmentioning

confidence: 99%

“…If ρ(u) = u then (1) reduces to the Lupaş operators defined in [8]. Ilarslan et al [7] gave uniform convergence results on a weighted space, where the weight function is φ(u) = 1 + ρ 2 (u) satisfying the conditions (ρ 1 ) and and (ρ 2 ) given above, in the sense of Gadjiev's results [9,10]. For the rate of convergence, the authors used a weighted modulus of continuity stated by Holhoş in [11] using the weight function.…”

Section: Introductionmentioning

confidence: 99%

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Approximation by Generalized Lupaş Operators Based on q-Integers

et al. 2020

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The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.

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“…Remark 1. We observe from Lemma 1 and Corollary 1, that for q = 1, we get the moments and central moments of generalized Lupaş operators [7].…”

Section: Proof By Taking Into Account the Recurrence Relationmentioning

confidence: 84%

“…Very recently motivated by the above work,İlarslan et al [7] introduced a new modification of Lupaş operators [8] using a suitable function ρ, which satisfies the following properties:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximation by Generalized Lupaş Operators Based on q-Integers

et al. 2020

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A new construction of Lupaş operators and its approximation properties

et al. 2021

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The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $ u m and $v_{m}$ v m of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$ [ 0 , ∞ ) . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

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Convergence of Generalized Lupaş-Durrmeyer Operators

et al. 2020

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The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on μ having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration.

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Generalized Lupaş operators

Cited by 3 publications

References 7 publications

Approximation by Generalized Lupaş Operators Based on q-Integers

Approximation by Generalized Lupaş Operators Based on q-Integers

A new construction of Lupaş operators and its approximation properties

Convergence of Generalized Lupaş-Durrmeyer Operators

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