Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Braha, Naim L.; Srivástava, H. M.; Et, Mikail

doi:10.1007/s12190-020-01398-5

Cited by 19 publications

(15 citation statements)

References 15 publications

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“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). Some other related recent developments on this subject can be found in [21][22][23][24].…”

Section: Preliminary Resultsmentioning

confidence: 99%

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

2021

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In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.

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“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). Some other related recent developments on this subject can be found in [21][22][23][24].…”

Section: Preliminary Resultsmentioning

confidence: 99%

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

2021

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“…Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature (see also Braha et al 16 and Mohiuddine et al 17 for some recent developments involving the Korovkin‐type and other approximation theorems).…”

Section: Introductionmentioning

confidence: 87%

Statistical product convergence of martingale sequences and its applications to Korovkin‐type approximation theorems

Srivástava

Jena

2021

Math Methods in App Sciences

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In this paper, we investigate and study the concepts of statistical product convergence and statistical product summability via deferred Cesàro and deferred weighted product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two nice and potentially useful concepts. Also, based upon our proposed concepts, we state and prove a set of new Korovkin‐type approximation theorems for a martingale sequence over a Banach space. Moreover, we demonstrate that our approximation theorems effectively extend and improve most (if not all) of the previously existing results (both in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature. We also suggest a direction for future researches on this subject, which are based upon the basic (or q‐) calculus, but not upon the trivial and inconsequential variations involving the so‐called (p, q)‐calculus.

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“…Fridy [5] considered statistical limit points and statistical cluster points of real number sequences. When we focus on the statistical convergence in the literature, we meet Fridy [6], Temizsu and Mikail [7], Braha et al [8], Nuray and Ruckle [9], Das et al [10], and so many other researchers (see [11][12][13]).…”

Section: Introductionmentioning

confidence: 94%

New Results on $I_{2}$ -Statistically Limit Points and

Kı̇şı̇

Huban

Gürdal

2021

Journal of Function Spaces

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In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

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Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Cited by 19 publications

References 15 publications

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Statistical product convergence of martingale sequences and its applications to Korovkin‐type approximation theorems

New Results on $I_{2}$ -Statistically Limit Points and

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Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Cited by 19 publications

References 15 publications

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Statistical product convergence of martingale sequences and its applications to Korovkin‐type approximation theorems

New Results on I 2 -Statistically Limit Points and

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New Results on $I_{2}$ -Statistically Limit Points and