Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 72 Sayı: 2, 438 - 448, 23.06.2023

Canan Sümbül Cemal Belen Mustafa Yıldırım

https://doi.org/10.31801/cfsuasmas.1124351

Öz

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Boos, J., Classical and modern methods in summability, Oxford University Press, Oxford, 2000.
  • 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
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Freedman, A. R., Sember, J. J., Densities and summability, Pacific J. Math., 95(2) (1981), 293-305.
  • Fridy, J. A., On statistical convergence, Analysis 5 (1985), 301-313.
  • Fridy, J.A., Statistical limit points, Proc. Amer. Math. Soc., 118(8) (1993), 1187-1193.
  • Listan-Garcia, M. C., f-statistical convergence, completeness and f-cluster points, Bull. Belg. Math. Soc. Simon Stevin, 23(2) (2016), 235-245.
  • Nakano, H., Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2) (1980), 139-150.
  • 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
  • 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
  • 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
  • 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

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

Yıl 2023, Cilt: 72 Sayı: 2, 438 - 448, 23.06.2023

Canan Sümbül Cemal Belen Mustafa Yıldırım

https://doi.org/10.31801/cfsuasmas.1124351

Öz

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.

Anahtar Kelimeler

$J_p$-statistical limit points $J_p$-statistical cluster points $f-J_p$-statistical limit points

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Boos, J., Classical and modern methods in summability, Oxford University Press, Oxford, 2000.
  • 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
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Freedman, A. R., Sember, J. J., Densities and summability, Pacific J. Math., 95(2) (1981), 293-305.
  • Fridy, J. A., On statistical convergence, Analysis 5 (1985), 301-313.
  • Fridy, J.A., Statistical limit points, Proc. Amer. Math. Soc., 118(8) (1993), 1187-1193.
  • Listan-Garcia, M. C., f-statistical convergence, completeness and f-cluster points, Bull. Belg. Math. Soc. Simon Stevin, 23(2) (2016), 235-245.
  • Nakano, H., Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2) (1980), 139-150.
  • 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
  • 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
  • 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
  • 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
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Canan Sümbül 0000-0002-8905-1247

Cemal Belen 0000-0002-8832-1524

Mustafa Yıldırım 0000-0002-8880-5457

Yayımlanma Tarihi 23 Haziran 2023
Gönderilme Tarihi 1 Haziran 2022
Kabul Tarihi 22 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 2

Kaynak Göster

APA 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, 72(2), 438-448. https://doi.org/10.31801/cfsuasmas.1124351
AMA Sümbül C, Belen C, Yıldırım M. On statistical limit points with respect to power series methods and modulus functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2023;72(2):438-448. doi:10.31801/cfsuasmas.1124351
Chicago Sümbül, Canan, Cemal Belen, ve Mustafa Yıldırım. “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 72, sy. 2 (Haziran 2023): 438-48. https://doi.org/10.31801/cfsuasmas.1124351.
EndNote Sümbül C, Belen C, Yıldırım M (01 Haziran 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 72 2 438–448.
IEEE C. Sümbül, C. Belen, ve M. Yıldırım, “On statistical limit points with respect to power series methods and modulus functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 2, ss. 438–448, 2023, doi: 10.31801/cfsuasmas.1124351.
ISNAD Sümbül, Canan vd. “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 72/2 (Haziran 2023), 438-448. https://doi.org/10.31801/cfsuasmas.1124351.
JAMA Sümbül C, Belen C, Yıldırım M. On statistical limit points with respect to power series methods and modulus functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:438–448.
MLA Sümbül, Canan vd. “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, c. 72, sy. 2, 2023, ss. 438-4, doi:10.31801/cfsuasmas.1124351.
Vancouver Sümbül C, Belen C, Yıldırım M. On statistical limit points with respect to power series methods and modulus functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):438-4.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.