Rough weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">I</mml:mi></mml:math>-αβ-statistical convergence in locally solid Riesz spaces

Ghosal, Sanjoy; Mandal, Sourav

doi:10.1016/j.jmaa.2021.125681

Cited by 3 publications

(4 citation statements)

References 37 publications

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“…Now, using the above assumption about the implications in ( 5) to (7) and by Definition 2, the right-hand side of ( 16) tends to zero as n → ∞. Consequently, we get…”

Section: Korovkin-type Approximation Theorems Via the W (δ(H K ; P ))...mentioning

confidence: 87%

“…belongs to C[0, 1] and is continuous on [0, 1], the implication given by (4) obviously implies (5) to (7).…”

Section: Korovkin-type Approximation Theorems Via the W (δ(H K ; P ))...mentioning

confidence: 99%

“…Furthermore, such a concept is closely related to the study of Real Analysis, Analytic Probability theory and Number theory, and so on. For some recent related developments on this subject, the reader can see, for example, the works in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Some Korovkin-Type Approximation Theorems Associated with a Certain Deferred Weighted Statistical Riemann-Integrable Sequence of Functions

Srivástava

Jena

2022

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Here, in this article, we introduce and systematically investigate the ideas of deferred weighted statistical Riemann integrability and statistical deferred weighted Riemann summability for sequences of functions. We begin by proving an inclusion theorem that establishes a relation between these two potentially useful concepts. We also state and prove two Korovkin-type approximation theorems involving algebraic test functions by using our proposed concepts and methodologies. Furthermore, in order to demonstrate the usefulness of our findings, we consider an illustrative example involving a sequence of positive linear operators in conjunction with the familiar Bernstein polynomials. Finally, in the concluding section, we propose some directions for future research on this topic, which are based upon the core concept of statistical Lebesgue-measurable sequences of functions.

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“…Now, using the above assumption about the implications in ( 5) to (7) and by Definition 2, the right-hand side of ( 16) tends to zero as n → ∞. Consequently, we get…”

Section: Korovkin-type Approximation Theorems Via the W (δ(H K ; P ))...mentioning

confidence: 87%

“…belongs to C[0, 1] and is continuous on [0, 1], the implication given by (4) obviously implies (5) to (7).…”

Section: Korovkin-type Approximation Theorems Via the W (δ(H K ; P ))...mentioning

confidence: 99%

See 1 more Smart Citation

Some Korovkin-Type Approximation Theorems Associated with a Certain Deferred Weighted Statistical Riemann-Integrable Sequence of Functions

Srivástava

Jena

2022

Axioms

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“…Recently, authors [30] explored the αβ-statistical convergence of order γ to investigate modified discrete operator approximation properties. For further study of αβ-statistical convergence of order γ, the readers can go through [6,8,13,28].…”

Section: Introductionmentioning

confidence: 99%

On Rough I–αβ–Statistical Convergence of Order γ in Intuitionistic Fuzzy Normed Spaces

Khan,

Rahaman,

Hazarika

2024

Preprint

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The concept of “αβ–statistical convergence of order γ” was developed by Aktug˘lu [1]. In this research article, we introduced the notion of “rough I–αβ–statistical convergence order γ” in the setting of intuitionistic fuzzy normed spaces. We find that the limit of this novel convergence is a set rather than a unique point. The study proves that the limit set is convex and closed with respect to the intuitionistic fuzzy norm. Moreover, we propose the notion of Ir– stγαβ –cluster points and establish the connections between the set of such cluster points and limit set of the above–mentioned convergence.

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Approximity of asymmetric metric spaces

Ghosal

Mandal

Banerjee³

2022

Mathematica Slovaca

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In this present work, we perceive the ideas of rough weighted statistical limit set as well as rough weighted statistical cluster points set and originate these conceptions into asymmetric metric spaces. On this context we frame out several results which substantially intensify these perceptions. While explicating such notions in terms of their asymmetric concepts, this generalization despite unfollows some previous results rather generates new characteristics. Also, we will adorn a sufficient condition using rough weighted statistical convergence which converts asymmetric metric spaces to approximate metric spaces.

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Rough weighted I-αβ-statistical convergence in locally solid Riesz spaces

Cited by 3 publications

References 37 publications

Some Korovkin-Type Approximation Theorems Associated with a Certain Deferred Weighted Statistical Riemann-Integrable Sequence of Functions

Some Korovkin-Type Approximation Theorems Associated with a Certain Deferred Weighted Statistical Riemann-Integrable Sequence of Functions

On Rough I–αβ–Statistical Convergence of Order γ in Intuitionistic Fuzzy Normed Spaces

Approximity of asymmetric metric spaces

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