Density by Moduli and Lacunary Statistical Convergence

Vinod K. Bhardwaj and Shweta Dhawan

Abstract and Applied Analysis, 2016, vol. 2016, 1-11

Abstract:

We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary strong convergence with respect to a modulus and -lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which , where and denote the sets of all -lacunary statistically convergent sequences and -statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of -statistical convergence is given. Finally, we give an -analog of the Cauchy criterion for convergence and a Tauberian theorem for -convergence is also proved.

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2016/9365037.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2016/9365037.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:9365037

DOI: 10.1155/2016/9365037

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().