KaydedilenlerDerginizi ekleyin

Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 2

On statistical limit points with respect to power series methods and modulus functions

Canan Sümbül(SİVAS CUMHURİYET ÜNİVERSİTESİ)0000-0002-8905-1247
Cemal Belen(ORDU ÜNİVERSİTESİ)0000-0002-8832-1524
Mustafa Yıldırım(SİVAS CUMHURİYET ÜNİVERSİTESİ)0000-0002-8880-5457
Sayfa
—
Yayın Tarihi
2023-06-23
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Namely, we define $f-J_p$-statistical limit and cluster points of the real sequences and compare the set of these limit points with the set of ordinary points.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we define a new type of statistical limit point using the notions of statistical convergence with respect to the $J_p$ power series method and then we present some examples to show the relations between these points and ordinary limit points.
📊
Temel Bulgular & Veri:After that we also study statistical limit points of a sequence with the help of a modulus function in the sense of the $J_p$ power series method.
💡
Sonuç & Katkı:Namely, we define $f-J_p$-statistical limit and cluster points of the real sequences and compare the set of these limit points with the set of ordinary points.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$J_p$-statistical limit points · $J_p$-statistical cluster points · $f-J_p$-statistical limit points

Abstract

In this study, we define a new type of statistical limit point using the notions of statistical convergence with respect to the $J_p$ power series method and then we present some examples to show the relations between these points and ordinary limit points. After that we also study statistical limit points of a sequence with the help of a modulus function in the sense of the $J_p$ power series method. Namely, we define $f-J_p$-statistical limit and cluster points of the real sequences and compare the set of these limit points with the set of ordinary points.

🔖

Bu Makaleye Atıf Yap

Sümbül, C., Belen, C., Yıldırım, M. (2023). On statistical limit points with respect to power series methods and modulus functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 2. https://doi.org/10.31801/cfsuasmas.1124351

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. Aizpuru, A., Listan-Garcia, M. C., Rambla-Barreno F., Density by moduli and statistical convergence, Quaestiones Mathematicae, 37 (2014), 525-530. https://doi.org/10.2989/16073606.2014.981683
  2. Arif, A., Yurdakadim, T., Approximation results on nonlinear operators by $P_p$-statistical convergence, Advanced Studies: Euro-Tbilisi Mathematical Journal, 15(3) (2022), 1-10. DOI:10.32513/asetmj/19322008220
  3. Bayram, N. Ş., Criteria for statistical convergence with respect to power series methods, Positivity. 25, (2021), 1097-1105. https://doi.org/10.1007/s11117-020-00801-6
  4. Bayram, N. Ş., Yıldız, S., Approximation by statistical convergence with respect to power series methods, Hacet. J. Math. Stat., 51(4) (2022), 1108-1120. DOI: 10.15672/hujms.1022072
  5. Bayram, N. Ş., P-strong convergence with respect to an Orlicz function, Turk J Math., 46 (2022), 832-838. https://doi.org/10.55730/1300-0098.3126
  6. Belen, C., Yıldırım, M., Sümbül, C., On statistical and strong convergence with respect to a modulus function and a power series method, Filomat, 34(12) (2020), 3981-3993. https://doi.org/10.2298/FIL2012981B
  7. Boos, J., Classical and modern methods in summability, Oxford University Press, Oxford, 2000.
  8. Demirci, K., Dirik, F., Yıldız, S., Approximation via equi-statistical convergence in the sense of power series method, RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. R, 116(65) (2022). https://doi.org/10.1007/s13398-021-01191-4
  9. Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  10. Freedman, A. R., Sember, J. J., Densities and summability, Pacific J. Math., 95(2) (1981), 293-305.
  11. Fridy, J. A., On statistical convergence, Analysis 5 (1985), 301-313.
  12. Fridy, J.A., Statistical limit points, Proc. Amer. Math. Soc., 118(8) (1993), 1187-1193.
  13. Listan-Garcia, M. C., f-statistical convergence, completeness and f-cluster points, Bull. Belg. Math. Soc. Simon Stevin, 23(2) (2016), 235-245.
  14. Nakano, H., Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  15. Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2) (1980), 139-150.
  16. Söylemez, D., A Korovkin type approximation theorem for Bal´azs Type Bleimann, Butzer and Hahn Operators via power series statistical convergence, Math. Slovaca, 72(1) (2022), 153-164. https://doi.org/10.1515/ms-2022-0011
  17. Sümbül, C., Belen, C., Yıldırım, M., Properties of $J_p$-statistical convergence, Cumhuriyet Sci. J., 43(2) (2022), 294-298. https://doi.org/10.17776/csj.1064559
  18. Ünver, M., Orhan, C., Statistical convergence with respect to power series methods and applications to approximation theory, Numer. Func. Anal Opt., 40(5) (2019), 535-547. https://doi.org/10.1080/01630563.2018.1561467
  19. Ünver, M., Bayram, N. Ş., On statistical convergence with respect to power series methods, Positivity (2022), 26-55. https://doi.org/10.1007/s11117-022-00921-1