Density by moduli and statistical boundedness
type: Item
instance of: scholarly article
title: Density by moduli and statistical boundedness
zbMATH Open document ID: 1470.40014
DOI: 10.1155/2016/2143018
author: V. K. Bhardwaj
author: Shweta Dhawan
author: Sandeep Gupta
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We have generalized the notion of statistical boundedness by introducing the concept of \(f\)-statistical boundedness for scalar sequences where \(f\) is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are \(f\)-statistically bounded for every unbounded modulus \(f\). A decomposition theorem for \(f\)-statistical convergence for vector valued sequences and a structure theorem for \(f\)-statistical boundedness have also been established.
Mathematics Subject Classification ID: 40A35
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 6929352
Wikidata QID: Q59121512
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/2143018
OpenAlex ID: W2263153394
cites work: Sur la convergence statistique
cites work: The Integrability of Certain Functions and Related Summability Methods
cites work: Double density by moduli and statistical convergence
cites work: Density by moduli and statistical convergence
cites work: On weak statistical convergence
cites work: STRONG INVARIANT A-SUMMABILITY WITH RESPECT TO A SEQUENCE OF MODULUS FUNCTIONS IN A SEMINORMED SPACE
cites work: \(f\)-statistical convergence of order \(\alpha\) and strong Cesàro summability of order \(\alpha\) with respect to a modulus
cites work: On some generalizations of statistical boundedness
cites work: On lacunary statistical boundedness
cites work: On \({\lambda}\)-statistical convergence of order \({\alpha}\) of sequences of function
cites work: Statistical convergence of double sequences on probabilistic normed spaces
cites work: Statistical convergence on intuitionistic fuzzy normed spaces
cites work: $\bar \lambda $-statistically convergent double sequences in probabilistic normed spaces
cites work: Q3867858
cites work: ON STATISTICAL CONVERGENCE
cites work: Statistical limit superior and limit inferior
cites work: Q4209729
cites work: Concave modulars
cites work: FK Spaces in Which the Sequence of Coordinate Vectors is Bounded
cites work: Inclusions between FK spaces and Kuttner's theorem
cites work: On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
cites work: Q4299503
cites work: Q4886933
cites work: \(F\)-seminormed sequence spaces defined by a sequence of modulus functions and strong summability
cites work: On some vector valued sequence spaces defined using a modulus function
cites work: Some sequence spaces defined by \(|\overline N,p_n|\) summability and a modulus function
cites work: Banach space valued sequence spaces defined by a modulus
cites work: Lacunary strong convergence of difference sequences with respect to a modulus function
cites work: Q5462014
cites work: Density by moduli and Wijsman lacunary statistical convergence of sequences of sets
cites work: THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES
cites work: Q3878090
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description: scientific article; zbMATH DE number 6929352