On the space of real valued statistically convergent sequences

The aim of this paper is to introduce an equivalence relation on the space of real valued statistically convergence sequences, Cst, and an inner product on the set of its equivalence classes. We equip Cst with the induced J- metric, dJ, by the given inner product. We prove that Cst is a complete J-metric space. We also show that the space of all real valued convergent sequences is a dense subspace of (Cst, dJ).

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Work Title On the space of real valued statistically convergent sequences
Access
Open Access
Creators
  1. Y. Sohooly
  2. Khadijeh Jahedi
  3. Aliasghar Alikhani-Koopaei
Keyword
  1. Natural density of sets
  2. Statistically convergence
  3. Equivalence relation
  4. Quotient space
License CC BY 4.0 (Attribution)
Work Type Article
Publisher
  1. Journal of Mathematical Extension
Publication Date February 1, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.30495/JME.2022.1572
Deposited February 01, 2024

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Version 1
published

  • Created
  • Added 16-Sohouli-Jahedi-Alikhani-1.pdf
  • Added Creator Yousef Sohooly
  • Added Creator Khadijeh Jahedi
  • Added Creator Aliasghar Alikhani-Koopaei
  • Published
  • Updated Keyword Show Changes
    Keyword
    • Natural density of sets, Statistically convergence, Equivalence relation, Quotient space
  • Renamed Creator Y. Sohooly Show Changes
    • Yousef Sohooly
    • Y. Sohooly
  • Updated