Generalized Baskakov type operators

Erençin, Ayşegül; Olgun, Ali; Taşdelen, Fatma

doi:10.1515/ms-2017-0048

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…Section 4.1), Aral, Ulusoy, and Deniz generalize the operators , extending in this way the results contained in [7,32]. See [35] for a modification of Baskakovtype operators in the spirit of what has been done for . We want to emphasize that the above constructions based on fixing suitable increasing functions do not recover the interesting case of linear operators fixing exponential functions, which has been a new and very popular direction in this research area in the last few years.…”

Section: A Brief Historymentioning

confidence: 78%

On Sequences of J. P. King-Type Operators

Acar

Montano

Garrancho

et al. 2019

Journal of Function Spaces

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This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King’s approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators.

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Section: A Brief Historymentioning

confidence: 78%

On Sequences of J. P. King-Type Operators

Acar

Montano

Garrancho

et al. 2019

Journal of Function Spaces

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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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