On $$\mu $$-deferred statistical convergence and strongly deferred summable functions

Et, Mikail; Baliarsingh, P.; Kandemir, Hacer Şengül; Küçükaslan, Mehmet

doi:10.1007/s13398-020-00983-4

Cited by 17 publications

(4 citation statements)

References 19 publications

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“…Moreover, Küçükaslan and Ylmaztürk delved into the concept of deferred statistical convergence in [14], paving the way for further investigations in this area. Several other works have also contributed to the theory of statistical convergence [1,[10][11][12][13]15].…”

Section: Introduction and Introductory Factsmentioning

confidence: 99%

Deferred statistical order convergence in Riesz spaces

Küçükaslan,

Aydın

2024

Hacettepe Journal of Mathematics and Statistics

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In recent years, researchers have focused on exploring different forms of statistical convergence in Riesz spaces, such as statistical order convergence and statistical unbounded order convergence. This study aims to present the concept of deferred statistical convergence within Riesz spaces, specifically concerning its relationship with order convergence. Furthermore, we delve into the interconnections between deferred statistical order convergence and various other types of statistical convergence. Moreover, we explore in depth the intricate connections between deferred statistical order convergence and other notable forms of statistical convergence. We provide valuable insights into the broader framework of statistical convergence theory in Riesz spaces.

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Section: Introduction and Introductory Factsmentioning

confidence: 99%

Deferred statistical order convergence in Riesz spaces

Küçükaslan,

Aydın

2024

Hacettepe Journal of Mathematics and Statistics

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“…They also introduced the notion of strongly deferred Cesàro convergence of sequences defined by modulus function 𝑓 and investigated its relation with deferred 𝑓-statistical convergence. We refer to [15][16][17][18][19][20][21][22] for additional different works on deferred statistical convergence.…”

Section: Introductionmentioning

confidence: 99%

On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function

Belen,

Yıldırım

2023

Cumhuriyet Science Journal

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Let f be any modulus function. We prove that the classes of strongly deferred Cesàro convergent sequences defined by f and deferred statistical convergent sequences are equivalent if the sequence is f-deferred uniformly integrable. Some converse inclusions are obtained when the modulus function f is compatible. Finally, for any compatible modulus f, we prove that any sequence is f-strongly deferred Cesàro convergent if and ony if it is deferred f-statistically convergent and deferred uniformly integrable.

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“…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%

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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On $$\mu $$-deferred statistical convergence and strongly deferred summable functions

Cited by 17 publications

References 19 publications

Deferred statistical order convergence in Riesz spaces

Deferred statistical order convergence in Riesz spaces

On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function

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

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