Research Article
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On a Generalization of Statistical Convergence of Double Sequences

Year 2024, Volume: 8 Issue: 2, 131 - 136, 30.12.2024
https://doi.org/10.47137/usufedbid.1520306

Abstract

In this study, the concept of delta convergence, which is a generalization of the statistical
convergence of double sequences is introduced. In connection with this, C_{\Delta} and Wp function
spaces, which consist of some functions of two-variables, are introduced and the relationship
between them is examined.

References

  • Fast H. Sur la Convergence Statistique, Colloquium Mathematicae, 1951;(2):241-244.
  • Schonberg I. J. The Integrability of Certain Functions and Related Summability Methods, Amer. Math. Monthly 1959;(66):361-375.
  • Sǎlát T. On Statistically Convergent Sequences of Real Numbers, Mathematica Slovaca, 1980;(30):139-150.
  • Fridy J. A. On Statistical Convergence, Analysis, 1985;(5):301-313.
  • Connor J. S. The Statistical and Strong p-Cesàro Convergence of Sequences, Analysis, 1988;(8):47-63.
  • Mursaleen O. H. H. Edely, Statistical Convergence of Double Sequences, 2003;(288):223-231.
  • Seyyidoğlu M. S, Tan N. Ö. A Note on Statistical Convergence on Time Scale, J, Inequal. Appl. 2012; Article ID 219.
  • Turan C, Duman O. Convergence Methods on Time Scales, AIP Conference Proceedings, American Institute of Physics, 2013;1120-1123.
  • Altin Y, Koyunbakan H, Yilmaz E. Uniform Statistical Convergence on Time Scales, J. Appl. Math. 2014; Article ID 471437.
  • Yilmaz E, Altin Y, Koyunbakan H, λ-Statistical Convergence on Time Scales, DCDIS Mathematical Analysis, 2016;(23):69-78.
  • Basarir M, A Note on the (θ,φ)-Statistical Convergence of the Product Time Scale, Konuralp Journal of Mathematics, 2020;(8.1):192-196.
  • Bohner M, Peterson A. Dynamic Equations on Time Scales, 2021;Birkäuser.
  • Bohner M, Peterson A. Advances in Dynamic Equations on Time Scales, 2023; Birkäuser.
  • Hilger S, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmanningfaltigkeiten, PhD thesis, University of Würzburg, 1988.

Çift İndisli Dizilerin İstatistiksel Yakınsaklığının Bir Genelleştirilmesi Üzerine

Year 2024, Volume: 8 Issue: 2, 131 - 136, 30.12.2024
https://doi.org/10.47137/usufedbid.1520306

Abstract

Bu çalışmada çift indisli dizilerin istatistiksel yakınsaklığının bir genelleştirilmesi olan delta yakınsaklık kavramı verilmiştir. Bu bağlamda iki değişkenli bazı fonksiyonlardan oluşan C_{\Delta} ve Wp fonksiyon uzayları tanıtılmış ve aralarındaki ilişkiler incelenmiştir.

References

  • Fast H. Sur la Convergence Statistique, Colloquium Mathematicae, 1951;(2):241-244.
  • Schonberg I. J. The Integrability of Certain Functions and Related Summability Methods, Amer. Math. Monthly 1959;(66):361-375.
  • Sǎlát T. On Statistically Convergent Sequences of Real Numbers, Mathematica Slovaca, 1980;(30):139-150.
  • Fridy J. A. On Statistical Convergence, Analysis, 1985;(5):301-313.
  • Connor J. S. The Statistical and Strong p-Cesàro Convergence of Sequences, Analysis, 1988;(8):47-63.
  • Mursaleen O. H. H. Edely, Statistical Convergence of Double Sequences, 2003;(288):223-231.
  • Seyyidoğlu M. S, Tan N. Ö. A Note on Statistical Convergence on Time Scale, J, Inequal. Appl. 2012; Article ID 219.
  • Turan C, Duman O. Convergence Methods on Time Scales, AIP Conference Proceedings, American Institute of Physics, 2013;1120-1123.
  • Altin Y, Koyunbakan H, Yilmaz E. Uniform Statistical Convergence on Time Scales, J. Appl. Math. 2014; Article ID 471437.
  • Yilmaz E, Altin Y, Koyunbakan H, λ-Statistical Convergence on Time Scales, DCDIS Mathematical Analysis, 2016;(23):69-78.
  • Basarir M, A Note on the (θ,φ)-Statistical Convergence of the Product Time Scale, Konuralp Journal of Mathematics, 2020;(8.1):192-196.
  • Bohner M, Peterson A. Dynamic Equations on Time Scales, 2021;Birkäuser.
  • Bohner M, Peterson A. Advances in Dynamic Equations on Time Scales, 2023; Birkäuser.
  • Hilger S, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmanningfaltigkeiten, PhD thesis, University of Würzburg, 1988.
There are 14 citations in total.

Details

Primary Language English
Subjects Real and Complex Functions (Incl. Several Variables)
Journal Section Research Article
Authors

Mustafa Seyyit Seyyidoğlu 0000-0001-9129-1373

Publication Date December 30, 2024
Submission Date July 22, 2024
Acceptance Date September 11, 2024
Published in Issue Year 2024 Volume: 8 Issue: 2

Cite

APA Seyyidoğlu, M. S. (2024). On a Generalization of Statistical Convergence of Double Sequences. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi, 8(2), 131-136. https://doi.org/10.47137/usufedbid.1520306
AMA Seyyidoğlu MS. On a Generalization of Statistical Convergence of Double Sequences. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. December 2024;8(2):131-136. doi:10.47137/usufedbid.1520306
Chicago Seyyidoğlu, Mustafa Seyyit. “On a Generalization of Statistical Convergence of Double Sequences”. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi 8, no. 2 (December 2024): 131-36. https://doi.org/10.47137/usufedbid.1520306.
EndNote Seyyidoğlu MS (December 1, 2024) On a Generalization of Statistical Convergence of Double Sequences. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi 8 2 131–136.
IEEE M. S. Seyyidoğlu, “On a Generalization of Statistical Convergence of Double Sequences”, Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi, vol. 8, no. 2, pp. 131–136, 2024, doi: 10.47137/usufedbid.1520306.
ISNAD Seyyidoğlu, Mustafa Seyyit. “On a Generalization of Statistical Convergence of Double Sequences”. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi 8/2 (December 2024), 131-136. https://doi.org/10.47137/usufedbid.1520306.
JAMA Seyyidoğlu MS. On a Generalization of Statistical Convergence of Double Sequences. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. 2024;8:131–136.
MLA Seyyidoğlu, Mustafa Seyyit. “On a Generalization of Statistical Convergence of Double Sequences”. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi, vol. 8, no. 2, 2024, pp. 131-6, doi:10.47137/usufedbid.1520306.
Vancouver Seyyidoğlu MS. On a Generalization of Statistical Convergence of Double Sequences. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. 2024;8(2):131-6.