Bulletin of the Belgian Mathematical Society - Simon Stevin

Density by moduli and Wijsman statistical convergence

Vinod K. Bhardwaj, Shweta Dhawan, and Oleksiy A. Dovgoshey

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Abstract

In this paper, we have generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence of these sets, where $f$ is an unbounded modulus. It is shown that the Wijsman convergent sequences are precisely those sequences which are $f$-Wijsman statistically convergent for every unbounded modulus $f$. We have also introduced a new concept of Wijsman strong Cesàro summability with respect to a modulus $f$, and investigate the relationship between the $f$-Wijsman statistically convergent sequences and the Wijsman strongly Cesàro summable sequences with respect to $f$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 3 (2017), 393-415.

Dates
First available in Project Euclid: 27 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1506477689

Digital Object Identifier
doi:10.36045/bbms/1506477689

Mathematical Reviews number (MathSciNet)
MR3706809

Zentralblatt MATH identifier
1382.40012

Subjects
Primary: 40A35: Ideal and statistical convergence [See also 40G15] 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45] 40G15: Summability methods using statistical convergence [See also 40A35]

Keywords
modulus function natural density statistical convergence strong Cesàro summability Wijsman convergence

Citation

Bhardwaj, Vinod K.; Dhawan, Shweta; Dovgoshey, Oleksiy A. Density by moduli and Wijsman statistical convergence. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 3, 393--415. doi:10.36045/bbms/1506477689. https://projecteuclid.org/euclid.bbms/1506477689


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