A Korovkin-Type Approximation Theorem and Power Series Method

In this paper we consider power series method which is also member of the class of all continuous summability methods. The power series method includes Abel method as well as Borel method. We investigate, using the power series method, Korovkin type approximation theorems for the sequence of positive linear operators defined on C[a, b] and L q [a, b], 1 ≤ q < ∞, respectively. We also study some quantitative estimates for L q approximation and give the rate of convergence of these operators.

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“…The next theorem is a particular case of Theorem 1 of [12]. For the completeness, we give the proof of our theorem by using an alternative way.…”

Section: Approximation Properties On C[ab] Via Power Series Methodsmentioning

confidence: 94%

Korovkin type approximation theorems via power series method

Taş

Atlıhan

2017

São Paulo J. Math. Sci.

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“…Recently, the power series summability method of convergence has attracted the researchers due to its nature of generality over the classical convergence [23]. For the interested reader, we refer to [15,21,22]. The following result shows the convergence of our operators…”

Section: Power Series Summability Approximation Process Viamentioning

confidence: 91%

On some summability methods for a q-analogue of an integral type operator based on multivariate q-Lagrange polynomials

Agrawal¹,

Shukla²,

Baxhaku³

2021

Preprint

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“…The important results in approximation theory have also been studied by using different concepts of convergences such as statistical convergence, ideal convergence, summation process [3,4,8,11,20,24]. It is effective to use these concepts since they make a nonconvergent sequence to converge.…”

Section: Introductionmentioning

confidence: 99%

Approximation for $q$-Chlodowsky Operators via Statistical Convergence with Respect to Power Series Method

TAŞER

Yurdakadim

2022

Mathematical Sciences and Applications E-Notes

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Many results which are obtained or unable to obtained by classical calculus have also been studied by q-calculus. It is effective to use q-calculus since it acts as a bridge between mathematics and physics. The q-analog of Chlodowsky operators has been introduced and the approximation properties of these operators have been studied in [12]. Then in [23], the q-analog of Stancu-Chlodowsky operators has been introduced and some approximation results of these operators have been studied via A-statistical convergence which is a more general setting. In this paper, we present the approximation properties of q-Chlodowsky operators via statistical convergence with respect to power series method. It is noteworthy to mention that statistical convergence and statistical convergence with respect to power series method are incompatible.

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A Korovkin-Type Approximation Theorem and Power Series Method

Cited by 18 publications

References 7 publications

Korovkin type approximation theorems via power series method

Korovkin type approximation theorems via power series method

On some summability methods for a q-analogue of an integral type operator based on multivariate q-Lagrange polynomials

Approximation for $q$-Chlodowsky Operators via Statistical Convergence with Respect to Power Series Method

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