Yıl 2023,
Cilt: 72 Sayı: 2, 438 - 448, 23.06.2023
Canan Sümbül
,
Cemal Belen
,
Mustafa Yıldırım
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
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.
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