ON A SEQUENCE OF KANTOROVICH TYPE OPERATORS VIA RIEMANN TYPE q-INTEGRAL

Başcanbaz‐Tunca, Gülen; Erençin, Ayşegül; Taşdelen, Fatma

doi:10.4134/bkms.2014.51.2.303

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…The application of (p; q)-calculus to well known operators magnetizes great attention of researchers. We can refer some of the recent papers as [1], [2], [6], [8], [10], [11], [14], [18] and [19]. Let us brie ‡y mention some notations and de…nitions of (p; q)-calculus.…”

Section: Introductionmentioning

confidence: 99%

On Stancu type generalization of (p,q)-Baskakov-Kantorovich operators

Kanat

Sofyalıoğlu

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In the current paper, we introduce Stancu type generalization of Baskakov-Kantorovich operators based on (p; q)-integers and estimate the moments. We show the convergence of the new operators via the weighted Korovkin theorem. Then we investigate direct results by using Peetre's Kfunctional and modulus of continuity. In addition, we give pointwise estimation by the help of functions belonging to Lipschitz class. Moreover, we demonstrate the Voronovskaya-type theorem for the newly constructed operators. In the last section, we represent some illustrative graphics to show the convergence of the constructed operators to the selected function by using MATLAB.

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Section: Introductionmentioning

confidence: 99%

On Stancu type generalization of (p,q)-Baskakov-Kantorovich operators

Kanat

Sofyalıoğlu

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p,q)-integrals

Iliyas

Bhatt

Khan

et al. 2022

Filomat

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In this paper, Lupa? Bernstein-Kantorovich operators have been studied using Jackson and Riemann type (p,q)-integrals. It has been shown that (p, q)-integrals as well as Riemann type (p, q)-integrals are not well defined for 0 < q < p < 1 and thus further analysis is needed. Throughout the paper, the case 1 ? q < p < ? has been used. Advantages of using Riemann type (p, q)-integrals are discussed over general (p, q)-integrals. Lupa? Bernstein-Kantorovich operators constructed via Jackson integral need not be positive for every f ? 0. So to make these operators based on general (p, q)-integral positive, one need to consider strictly monotonically increasing functions, and to handle this situation Lupa? Bernstein-Kantorovich operators are constructed using Riemann type (p, q)-integrals. However Lupa? (p, q)-Bernstein-Kantorovich operators based on Riemann type (p, q)-integrals are always positive linear operators. Approximation properties for these operators based on Korovkin?s type approximation theorem are investigated. The rate of convergence via modulus of continuity and function f belonging to the Lipschitz class is computed.

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Integral Baskakov type operator with quadratic order of approximation

Gairola,

Singh

2023

MFC

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ON A SEQUENCE OF KANTOROVICH TYPE OPERATORS VIA RIEMANN TYPE q-INTEGRAL

Cited by 3 publications

References 25 publications

On Stancu type generalization of (p,q)-Baskakov-Kantorovich operators

On Stancu type generalization of (p,q)-Baskakov-Kantorovich operators

Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p,q)-integrals

Integral Baskakov type operator with quadratic order of approximation

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