Λ2-Weighted statistical convergence and Korovkin and Voronovskaya type theorems

“…Over the years, statistical convergence and its extensions have recently become an active research area in functional analysis. For more varied approaches to statistical convergence and its applications to approximation theorems, we refer to . The reader can also see, for more recent developments, such as the weighted statistical convergence based on generalized difference operator involving ( p , q )‐gamma function, statistical weighted B ‐summability and the relative weighted summability in modular function spaces.…”

Section: Statistical Approximation Properties For the Generalized Szamentioning

confidence: 99%

Approximation properties of the generalized Szasz operators by multiple Appell polynomials via power summability method

Braha

Kadak

2019

Math Methods in App Sciences

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In this paper some properties of the generalized Szasz operators by multiple Appell polynomials are given, using into consideration the power summability method. In the first section are given some direct estimation related to the generalized Szasz operators by multiple Appell polynomials, including Korovkin type theorem. In the second section, we give some results related to the weighted spaces of continuous functions and Voronovskaya type theorem. In the third section, we have proved some results related to the statistical convergence of the generalized Szasz operators by multiple Appell polynomials, using into consideration the A− transformation. At the end of the paper are given some illustrative computational examples which make such summability methods (for example, power series method) more useful and fruitful for applications of functional analysis in approximation theory.

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“…Some recent papers on the topic dealing with different classes of polynomials as well as Korovkin-type approximation theorems and Voronovskaja-type approximation theorems can be consulted by readers (cf. [6,7,10,[18][19][20][21]24]).…”

Section: )mentioning

confidence: 99%

Approximation by Chlodowsky type of Szász operators based on Boas–Buck-type polynomials

Mursaleen¹,

Al-Abied²,

Acu³

2018

Turk J Math

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A Chlodowsky variant of generalized Szász-type operators involving Boas-Buck-type polynomials is considered and some convergence properties of these operators by using a weighted Korovkin-type theorem are given. A Voronoskaja-type theorem is proved. The convergence properties of these operators in a weighted space of functions defined on [0, ∞) are studied. The theoretical results are exemplified choosing the special cases of Boas-Buck polynomials, namely Appell-type polynomials, Laguerre polynomials, and Charlier polynomials.

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Λ2-Weighted statistical convergence and Korovkin and Voronovskaya type theorems

Cited by 54 publications

References 12 publications

On weighted statistical convergence based on (p,q)-integers and related approximation theorems for functions of two variables

On weighted statistical convergence based on (p,q)-integers and related approximation theorems for functions of two variables

Approximation properties of the generalized Szasz operators by multiple Appell polynomials via power summability method

Approximation by Chlodowsky type of Szász operators based on Boas–Buck-type polynomials

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