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\(\mathcal {I}\)-Statistically Localized Sequence in 2-Normed Spaces

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Artificial Intelligence and Applied Mathematics in Engineering Problems (ICAIAME 2019)

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 43))

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Abstract

In 1974, Krivonosov defined the concept of localized sequence that is defined as a generalization of Cauchy sequence in metric spaces. In this work, by using the concept of ideal, the statistically localized sequences are defined and some basic properties of \(\mathcal {I}\)-statistically localized sequences are given. Also, it is shown that a sequence is \(\mathcal {I}\)-statistically Cauchy iff its statistical barrier is equal to zero.

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Author information

Authors and Affiliations

  1. Department of Statistics, Süleyman Demirel University, 32260, Isparta, Turkey

    Ulaş Yamancı

  2. Department of Mathematics, Süleyman Demirel University, 32260, Isparta, Turkey

    Mehmet Gürdal

Authors
  1. Ulaş Yamancı
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  2. Mehmet Gürdal
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Corresponding author

Correspondence to Mehmet Gürdal .

Editor information

Editors and Affiliations

  1. Department of ECE, Karunya University, Coimbatore, Tamil Nadu, India

    D. Jude Hemanth

  2. Department of Computer Engineering, Faculty of Engineering, Suleyman Demirel University, Isparta, Isparta, Turkey

    Utku Kose

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Yamancı, U., Gürdal, M. (2020). \(\mathcal {I}\)-Statistically Localized Sequence in 2-Normed Spaces. In: Hemanth, D., Kose, U. (eds) Artificial Intelligence and Applied Mathematics in Engineering Problems. ICAIAME 2019. Lecture Notes on Data Engineering and Communications Technologies, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-030-36178-5_92

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