Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

Alotaibi, Abdullah; Aljahili, Alaa Mohammed; Mohiuddine, S.A.

doi:10.28924/2291-8639-17-2019-711

Research Article

Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

Abdullah Alotaibi¹
Alaa Mohammed Aljahili¹
S.A. Mohiuddine¹*

King Abdulaziz University

* Corresponding author

Abstract

We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.

How to Cite

A. Alotaibi, A. M. Aljahili, S. A. Mohiuddine, Generalized Statistical Convergence of Double Sequences in Paranormed Spaces, Int. J. Anal. Appl. 17 (2019), 711–721. https://doi.org/10.28924/2291-8639-17-2019-711

BibTeX

@article{Alotaibi2019,
  author  = {Alotaibi, Abdullah and Aljahili, Alaa Mohammed and Mohiuddine, S.A.},
  title   = {Generalized Statistical Convergence of Double Sequences in Paranormed Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {711--721},
  doi     = {10.28924/2291-8639-17-2019-711}
}

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