Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 71 Sayı: 1, 1 - 12, 30.03.2022

Uğur Ulusu Erdinç Dündar Nimet Pancaroğlu Akın

https://doi.org/10.31801/cfsuasmas.903988

Öz

Kaynakça

  • Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(3) (1900), 289–321. https://doi.org/10.1007/BF01448977
  • Moricz, F., Statistical convergence of multiple sequences, Arc. Math, 81(1) (2003), 82–89. https://doi.org/10.1007/s00013-003-0506-9
  • Mursaleen, M., Edely, O. H. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1) (2003), 223–231. https://doi.org/10.1016/j.jmaa.2003.08.004
  • Patterson, R. F., Savaş, E., Lacunary statistical convergence of double sequences, Math. Commun. 10(1) (2005), 55–61.
  • Savaş, E., Patterson, R. F., Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl., 11(4) (2009), 610–615.
  • Patterson, R. F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2003), 469–478. https://doi.org/10.1007/s10012-002-0469-y
  • Wijsman, R. A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1) (1964), 186–188. https://doi.org/10.1090/S0002-9904-1964-11072-7
  • Baronti, M., Papini, P., Convergence of Sequences of Sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986.
  • Nuray, F., Rhoades, B. E., Statistical convergence of sequences of sets, Fasc. Math., 49(2) (2012), 87–99. https://doi.org/10.3968/j.pam.1925252820120402.2264
  • Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2(1) (1994), 77–94. https://doi.org/10.1007/BF01027094
  • Nuray, F., Ulusu, U., Dündar, E., Lacunary statistical convergence of double sequences of sets, Soft Comput., 20(7) (2016), 2883–2888. https://doi.org/10.1007/s00500-015-1691-8
  • Nuray, F., Ulusu, U., Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform., 28(2) (2019), 143–150. https://doi.org/10.37193/CMI.2019.02.06
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., 16(1) (2021), 55–64. https://doi.org/10.29252/ijmsi.16.1.55
  • Nuray, F., Patterson, R. F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Math., 49(2) (2016), 183–196. https://doi.org/10.1515/dema-2016-0016
  • Ulusu, U., Dündar, E., Asymptotically I2-lacunary statistical equivalence of double sequences of sets, J. Ineq. Spec. Funct., 7(2) (2016), 44–56.
  • Ulusu, U., Gülle, E., Wijsman asymptotical I2-statistically equivalent double set sequences of order η, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 854–862. https://doi.org/10.31801/cfsuasmas.695309
  • Gülle, E., Ulusu, U., Wijsman asymptotical I2-lacunary statistically equivalence of order η for double set sequences, J. Appl. Math. Inform., (in press) (2021).
  • Pancaroğlu, N., Nuray, F., Savaş, E., On asymptotically lacunary invariant statistical equivalent set sequences, AIP Conf. Proc., 1558(1) (2013), 780–781. https://doi.org/10.1063/1.4825609
  • Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, J. Math., 2013(Article ID 310438) (2013), 5 pages. https://doi.org/10.1155/2013/310438

Lacunary invariant statistical equivalence for double set sequences

Yıl 2022, Cilt: 71 Sayı: 1, 1 - 12, 30.03.2022

Uğur Ulusu Erdinç Dündar Nimet Pancaroğlu Akın

https://doi.org/10.31801/cfsuasmas.903988

Öz

In this paper, we introduce the notions of asymptotical strong σ2σ2-equivalence, asymptotical σ2σ2-statistical equivalence, asymptotical lacunary strong σ2σ2-equivalence and asymptotical lacunary σ2σ2-statistical equivalence in the Wijsman sense for double set sequences. Also, we investigate some relations between these new asymptotical equivalence notions.

Anahtar Kelimeler

Asymptotical equivalence double lacunary sequence invariant mean statistical convergence convergence in the Wijsman sense

Kaynakça

  • Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(3) (1900), 289–321. https://doi.org/10.1007/BF01448977
  • Moricz, F., Statistical convergence of multiple sequences, Arc. Math, 81(1) (2003), 82–89. https://doi.org/10.1007/s00013-003-0506-9
  • Mursaleen, M., Edely, O. H. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1) (2003), 223–231. https://doi.org/10.1016/j.jmaa.2003.08.004
  • Patterson, R. F., Savaş, E., Lacunary statistical convergence of double sequences, Math. Commun. 10(1) (2005), 55–61.
  • Savaş, E., Patterson, R. F., Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl., 11(4) (2009), 610–615.
  • Patterson, R. F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2003), 469–478. https://doi.org/10.1007/s10012-002-0469-y
  • Wijsman, R. A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1) (1964), 186–188. https://doi.org/10.1090/S0002-9904-1964-11072-7
  • Baronti, M., Papini, P., Convergence of Sequences of Sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986.
  • Nuray, F., Rhoades, B. E., Statistical convergence of sequences of sets, Fasc. Math., 49(2) (2012), 87–99. https://doi.org/10.3968/j.pam.1925252820120402.2264
  • Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2(1) (1994), 77–94. https://doi.org/10.1007/BF01027094
  • Nuray, F., Ulusu, U., Dündar, E., Lacunary statistical convergence of double sequences of sets, Soft Comput., 20(7) (2016), 2883–2888. https://doi.org/10.1007/s00500-015-1691-8
  • Nuray, F., Ulusu, U., Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform., 28(2) (2019), 143–150. https://doi.org/10.37193/CMI.2019.02.06
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., 16(1) (2021), 55–64. https://doi.org/10.29252/ijmsi.16.1.55
  • Nuray, F., Patterson, R. F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Math., 49(2) (2016), 183–196. https://doi.org/10.1515/dema-2016-0016
  • Ulusu, U., Dündar, E., Asymptotically I2-lacunary statistical equivalence of double sequences of sets, J. Ineq. Spec. Funct., 7(2) (2016), 44–56.
  • Ulusu, U., Gülle, E., Wijsman asymptotical I2-statistically equivalent double set sequences of order η, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 854–862. https://doi.org/10.31801/cfsuasmas.695309
  • Gülle, E., Ulusu, U., Wijsman asymptotical I2-lacunary statistically equivalence of order η for double set sequences, J. Appl. Math. Inform., (in press) (2021).
  • Pancaroğlu, N., Nuray, F., Savaş, E., On asymptotically lacunary invariant statistical equivalent set sequences, AIP Conf. Proc., 1558(1) (2013), 780–781. https://doi.org/10.1063/1.4825609
  • Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, J. Math., 2013(Article ID 310438) (2013), 5 pages. https://doi.org/10.1155/2013/310438
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Uğur Ulusu 0000-0001-7658-6114

Erdinç Dündar 0000-0002-0545-7486

Nimet Pancaroğlu Akın 0000-0003-2886-3679

Yayımlanma Tarihi 30 Mart 2022
Gönderilme Tarihi 26 Mart 2021
Kabul Tarihi 1 Haziran 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 1

Kaynak Göster

APA Ulusu, U., Dündar, E., & Pancaroğlu Akın, N. (2022). Lacunary invariant statistical equivalence for double set sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 1-12. https://doi.org/10.31801/cfsuasmas.903988
AMA Ulusu U, Dündar E, Pancaroğlu Akın N. Lacunary invariant statistical equivalence for double set sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2022;71(1):1-12. doi:10.31801/cfsuasmas.903988
Chicago Ulusu, Uğur, Erdinç Dündar, ve Nimet Pancaroğlu Akın. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 1 (Mart 2022): 1-12. https://doi.org/10.31801/cfsuasmas.903988.
EndNote Ulusu U, Dündar E, Pancaroğlu Akın N (01 Mart 2022) Lacunary invariant statistical equivalence for double set sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 1–12.
IEEE U. Ulusu, E. Dündar, ve N. Pancaroğlu Akın, “Lacunary invariant statistical equivalence for double set sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 1, ss. 1–12, 2022, doi: 10.31801/cfsuasmas.903988.
ISNAD Ulusu, Uğur vd. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (Mart 2022), 1-12. https://doi.org/10.31801/cfsuasmas.903988.
JAMA Ulusu U, Dündar E, Pancaroğlu Akın N. Lacunary invariant statistical equivalence for double set sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:1–12.
MLA Ulusu, Uğur vd. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 1, 2022, ss. 1-12, doi:10.31801/cfsuasmas.903988.
Vancouver Ulusu U, Dündar E, Pancaroğlu Akın N. Lacunary invariant statistical equivalence for double set sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):1-12.

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

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