On I-statistically ϕ-convergence

Debnath, Shyamal; Choudhury, Chiranjib

doi:10.22199/issn.0717-6279-4036

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2024

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Cited by 4 publications

References 16 publications

(19 reference statements)

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Gradual Normed Linear Spaces

Debnath,

Choudhury

2024

Advances in Functional Analysis and Fixed-Point Theory

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Gradual Normed Linear Spaces

Debnath,

Choudhury

2024

Advances in Functional Analysis and Fixed-Point Theory

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Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences

Choudhury

2023

Journal of Applied Analysis

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Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of ℐ {\mathcal{I}} -statistical supremum and ℐ {\mathcal{I}} -statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions. We also introduce the concept of ℐ {\mathcal{I}} -statistical monotonicity and establish the condition under which an ℐ {\mathcal{I}} -statistical monotonic sequence is ℐ {\mathcal{I}} -statistical convergent. We end up giving a necessary and a sufficient condition for the ℐ {\mathcal{I}} -statistical convergence of a real-valued sequence.

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On λ-statistically φ-convergence

Choudhury,

Debnath,

Savaş

2023

Journal of Applied Analysis

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In this paper, by using the notions of λ-density, ( V , λ ) {(V,\lambda)} -summability and Orlicz function ϕ, we introduce a new concept of convergence, namely λ-statistically ϕ-convergence, as a generalization of the λ-statistical convergence and statistically ϕ-convergence. Based on this concept, we introduce a new sequence space S λ - ϕ {S_{\lambda}-\phi} and investigate some of its properties. Also, we find its relations with statistically ϕ-convergence, [ C , 1 ] ϕ {[C,1]_{\phi}} -summability and [ V , λ ] ϕ {[V,\lambda]_{\phi}} -summability. Finally, we introduce and investigate the concept of S λ - ϕ {S_{\lambda}-\phi} Cauchy sequences.

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On I-statistically ϕ-convergence

Abstract: In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.

Cited by 4 publications

References 16 publications

Gradual Normed Linear Spaces

Gradual Normed Linear Spaces

Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences

On λ-statistically φ-convergence

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