An Introductory Course in Summability Theory

Aasma, Ants; Dutta, Hemen; Natarajan, P.N.

doi:10.1002/9781119397786

Cited by 32 publications

(9 citation statements)

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“…Recently, some researchers have attempted to assign properties to AK, AB, KB, SAK, FAK, AD, UAB, UAK, USAK, and UFAK in FK spaces and topological properties of sequence spaces (see, e.g., [6,7]). Additional information and techniques on summability and related concepts can be found in [4,[8][9][10][11][12].…”

Section: Definitionmentioning

confidence: 99%

Some Functional Sections in Topological Sequence Spaces

Akdemir

Ersoy

Furkan

et al. 2022

Journal of Function Spaces

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Summability is a particularly fertile field for functional analysis application. Summability through functional analysis has become one of the most fascinating disciplines since it contains both interesting and challenging issues. In this paper, we aim to introduce four new sectional properties for topological sequence spaces: sectional weakly absolute convergence (WAC), sectional weak boundedness (WB), sectional weakly p -absolute convergence W p AC , and sectional weakly bounded variation (WBV). We have, also, investigate some of their relations and identities.

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Section: Definitionmentioning

confidence: 99%

Some Functional Sections in Topological Sequence Spaces

Akdemir

Ersoy

Furkan

et al. 2022

Journal of Function Spaces

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“…Recently, a few researchers are working in this direction over the probability space. For some current works, see [1], [14], [22], [23] and [26].…”

Section: Example 12mentioning

confidence: 99%

Equi-statistical convergence of a sequence of distribution functions via deferred Nörlund summability mean and associated approximation theorems

Jena

2021

Filomat

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In this paper, the notion of statistical point-wise convergence, equi-statistical convergence and statistical uniform convergence of a sequence of distribution functions via the deferred N?rlund summability mean has been introduced, and accordingly an inclusion relation between these interesting notions is established. Moreover, as an application point of view, a new Korovkin-type approximation theorem is proved via the deferred N?rlund equi-statistical convergence for the sequence of distribution functions. Also, some illustrative examples are considered to justify that the proposed theorem is a nontrivial extension of some well established Korovkin-type approximation theorems for sequence of real-valued functions. Finally, a number of interesting cases are highlighted in support of the definitions and outcomes.

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“…In particular, it is very much useful in the study of Machine Learning, Soft Computing, Number Theory, Measure theory, Probability Theory etc. For some recent research works in this direction, see [1], [3], [4], [7], [15], [16], [20] and [22] . Suppose J ⊆ N, and let J k = {ξ : ξ k and ξ ∈ J}.…”

Section: Introductionmentioning

confidence: 99%

A new approach to Korovkin-type theorems based on deferred Nörlund summability mean

Priyadarsini,

Bidu Bhusan,

Susanta Kumar

2023

AUCMCS

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This paper aims to introduce the notions of deferred Nörlund statistical Riemann integrability and statistical deferred Nörlund Riemann summability for sequence of real-valued functions and to apply them in Korovkin-type new approximations. First, we present an inclusion theorem to understand the connection between these new notions. Then, based on these potential notions we establish new versions of Korovkin-type theorems with three algebraic test functions. Finally, we compute an example, under the consideration of a positive linear operator in association with the Bernstein polynomials to exhibit the effectiveness of our findings.

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An Introductory Course in Summability Theory

Cited by 32 publications

References 0 publications

Some Functional Sections in Topological Sequence Spaces

Some Functional Sections in Topological Sequence Spaces

Equi-statistical convergence of a sequence of distribution functions via deferred Nörlund summability mean and associated approximation theorems

A new approach to Korovkin-type theorems based on deferred Nörlund summability mean

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