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

Canan Sümbül; Cemal Belen; Mustafa Yıldırım

doi:10.31801/cfsuasmas.1124351

Research Article

Year 2023, Volume: 72 Issue: 2, 438 - 448, 23.06.2023

Canan Sümbül Cemal Belen Mustafa Yıldırım

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

Abstract

References

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

Year 2023, Volume: 72 Issue: 2, 438 - 448, 23.06.2023

Canan Sümbül Cemal Belen Mustafa Yıldırım

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

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.

Keywords

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

References

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

There are 19 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Canan Sümbül 0000-0002-8905-1247 Cemal Belen 0000-0002-8832-1524 Mustafa Yıldırım 0000-0002-8880-5457
Publication Date	June 23, 2023
Submission Date	June 1, 2022
Acceptance Date	November 22, 2022
Published in Issue	Year 2023 Volume: 72 Issue: 2

Cite

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. June 2023;72(2):438-448. doi:10.31801/cfsuasmas.1124351
Chicago	Sümbül, Canan, Cemal Belen, and 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, no. 2 (June 2023): 438-48. https://doi.org/10.31801/cfsuasmas.1124351.
EndNote	Sümbül C, Belen C, Yıldırım M (June 1, 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, and M. Yıldırım, “On statistical limit points with respect to power series methods and modulus functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 2, pp. 438–448, 2023, doi: 10.31801/cfsuasmas.1124351.
ISNAD	Sümbül, Canan et al. “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 (June 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 et al. “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, vol. 72, no. 2, 2023, pp. 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.