Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

Çanak, İbrahim; Önder, Zerrin; Totur, Ümi̇t

doi:10.1007/s00025-016-0582-3

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…Otherwise, the notion of C,1,1,1 ðÞ summability of a triple sequence was originally introduced by Canak and Totur in 2016 [19]. Later, Canak et al [20] studied some C,1,1,1 ðÞ means of a statistical convergent triple sequence and gave some classical Tauberian theorems for a triple sequence that P-convergence follows from statistically C,1,1,1 ðÞ summability under the two-sided boundedness conditions and slowly oscillating conditions in certain senses. Then, in 2020 Totur and Canak [21] proved Tauberian conditions under which convergence of triple integrals follows from C,1,1,1 ðÞ summability.…”

Section: Introductionmentioning

confidence: 99%

Some Tauberian Theorems under Triple Statistically Nörlund-Cesáro Summability Method

Granados¹

2023

Functional Calculus - Recent Advances and Development

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In this paper, we extend the notion presented by Braha (2020) in a higher dimension, we introduce the notion of Np,qn,m,gCn,m,g1,1,1-statistically convergence and show necessity and sufficiency conditions under which the existence of the limit st-limn,m,g→∞xn,m,g=L follows from that st-limn,m,g→∞Np,qn,m,gCn,m,g1,1,1=L. These conditions are one-sided or two-sided if xn,m,g is a sequence of real or complex numbers, respectively.

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Section: Introductionmentioning

confidence: 99%

Some Tauberian Theorems under Triple Statistically Nörlund-Cesáro Summability Method

Granados¹

2023

Functional Calculus - Recent Advances and Development

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Tauberian Theorems for Sequences in 2-Normed Spaces

Savaş

Sezer

2017

Results Math

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Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

Sharma

Singh

Raj

2021

IFS

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The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1.

show abstract

Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

Cited by 4 publications

References 14 publications

Some Tauberian Theorems under Triple Statistically Nörlund-Cesáro Summability Method

Some Tauberian Theorems under Triple Statistically Nörlund-Cesáro Summability Method

Tauberian Theorems for Sequences in 2-Normed Spaces

Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

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