Voronoi means, moving averages, and power series

Bingham, Ν. H.; Gashi, Bujar

doi:10.1016/j.jmaa.2016.12.004

Cited by 3 publications

(2 citation statements)

References 51 publications

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“…Voronoi mean, is a non-regular generalisation of the Nörlund mean, has been introduced by Bingham and Gashi in [2]. Now, we remind this method: Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Voronoi mean and applications to approximation theorems

Demirci

Yıldız

Dirik

2021

AUCMCS

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In this paper, we give statistical Voronoi mean which is a new statistical summability method, is not need to be regular and positive. We prove a Korovkin type approximation theorem via this method that covers many important summability methods scattered in the literature. Also, we demonstrate that our theorem is stronger than proven by earlier authors with an interesting application. Finally, we establish the rate of convergence.

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“…Voronoi mean, is a non-regular generalisation of the Nörlund mean, has been introduced by Bingham and Gashi in [2]. Now, we remind this method: Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

“…Now, we remind this method: Definition 1.1. [2] Let the real sequences {p n , q n , u n } with u n = 0 for n ≥ 0, be given. The real sequence {s n } has Voronoi mean s, written…”

Section: Introductionmentioning

confidence: 99%

Statistical Voronoi mean and applications to approximation theorems

Demirci

Yıldız

Dirik

2021

AUCMCS

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Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass

Avena,

da Costa

2023

J Theor Probab

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We consider weighted sums of independent random variables regulated by an increment sequence and provide operative conditions that ensure a strong law of large numbers for such sums in both the centred and non-centred case. The existing criteria for the strong law are either implicit or based on restrictions on the increment sequence. In our setup we allow for an arbitrary sequence of increments, possibly random, provided the random variables regulated by such increments satisfy some mild concentration conditions. In the non-centred case, convergence can be translated into the behaviour of a deterministic sequence and it becomes a game of mass when the expectation of the random variables is a function of the increment sizes. We identify various classes of increments and illustrate them with a variety of concrete examples.

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Tauberian Korevaar

Bingham

2023

Indagationes Mathematicae

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Voronoi means, moving averages, and power series

Abstract: We introduce a non-regular generalisation of the Nörlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A strong law of large numbers is also proved

Cited by 3 publications

References 51 publications

Statistical Voronoi mean and applications to approximation theorems

Statistical Voronoi mean and applications to approximation theorems

Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass

Tauberian Korevaar

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