Banach and Statistical Cores of Bounded Sequences

Orhan, Cihan; Yardımcı, Şeyhmus

doi:10.1023/b:cmaj.0000027247.75771.b3

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…letting n → ∞ in (24) and using (22), (23) we have ∑ ∞ k=0 c nk x k → p, as n → ∞. This implies that C ∈ (st ∩ ∞ : c λ ) reg .…”

mentioning

confidence: 89%

“…(ii) C = (c nk ) ∈ (c : c λ ) reg if and only if (20) holds and (21), (22) also hold with α k = 0 for all k ∈ N and α = 1, respectively.…”

Section: λ-Corementioning

confidence: 99%

“…The notion of the statistical core (or st-core) of a complex valued sequence has been introduced by Fridy and Orhan [21] and it is shown for a statistically bounded sequence x that st − core(x) = z∈C C x (z) for any x ∈ ∞ , where C x (z) = {w ∈ C : |w − z| ≤ st − lim sup k |x k − z|}. The notion of statistically convergence was used by several authors [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Some new paranormed sequence spaces and core theorems

Karaisa

Başar

2014

AIP Conference Proceedings

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Let μ ∈ { ∞ , c, c 0 }. In this study, by using lambda matrix Λ and difference matrix B, we introduce the new nonabsolute type paranormed sequence space μ(λ , B; p) and prove that μ(λ , B; p) and μ(p) linearly isomorphic. Further, we give some inclusion relations concerning the space μ(λ , B; p). Afterwards, we determine the alpha-, beta-and gamma-duals of the space μ(λ , p; B). We also give the characterization of the classes (μ(λ , B; p) : ν) and (ν : μ(λ , B; p)), where ν is any given sequence space. Moreover, we introduce the Λ-core of a complex valued sequence and determine the necessary and sufficient conditions on a matrix A for which Λ − core(Ax) ⊆ K − core(x) and Λ − core(Ax) ⊆ st − core(x) for all x ∈ ∞ .

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“…letting n → ∞ in (24) and using (22), (23) we have ∑ ∞ k=0 c nk x k → p, as n → ∞. This implies that C ∈ (st ∩ ∞ : c λ ) reg .…”

mentioning

confidence: 89%

“…(ii) C = (c nk ) ∈ (c : c λ ) reg if and only if (20) holds and (21), (22) also hold with α k = 0 for all k ∈ N and α = 1, respectively.…”

Section: λ-Corementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some new paranormed sequence spaces and core theorems

Karaisa

Başar

2014

AIP Conference Proceedings

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Multidimensional matrix characterizations of the Banach and Pringsheim core

Patterson

Savaş

2007

Applied Mathematics Letters

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On uniform statistical convergence

Gülfırat

Bayram

2023

Georgian Mathematical Journal

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This paper is a continuation of the so far performed studies on the concept of uniform statistical convergence. We first characterize two inequalities concerning the uniform statistical limit superior that lead to two core inclusion results for bounded real sequences. Using the inverse Fourier transformation, we also give a criterion on uniform statistical convergence, and study some factorization results of the space of uniformly statistically convergent sequences. These results are used to give a Korovkin-type approximation theorem.

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Banach and Statistical Cores of Bounded Sequences

Cited by 3 publications

References 21 publications

Some new paranormed sequence spaces and core theorems

Some new paranormed sequence spaces and core theorems

Multidimensional matrix characterizations of the Banach and Pringsheim core

On uniform statistical convergence

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