Lacunary invariant statistical equivalence for double set sequences

Uğur Ulusu; Erdinç Dündar; Nimet Pancaroğlu Akın

doi:10.31801/cfsuasmas.903988

Research Article

Year 2022, Volume: 71 Issue: 1, 1 - 12, 30.03.2022

Uğur Ulusu Erdinç Dündar Nimet Pancaroğlu Akın

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

Abstract

References

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

Year 2022, Volume: 71 Issue: 1, 1 - 12, 30.03.2022

Uğur Ulusu Erdinç Dündar Nimet Pancaroğlu Akın

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

Abstract

In this paper, we introduce the notions of asymptotical strong $σ_{2}$ -equivalence, asymptotical $σ_{2}$ -statistical equivalence, asymptotical lacunary strong $σ_{2}$ -equivalence and asymptotical lacunary $σ_{2}$ -statistical equivalence in the Wijsman sense for double set sequences. Also, we investigate some relations between these new asymptotical equivalence notions.

Keywords

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

References

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

There are 19 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Uğur Ulusu 0000-0001-7658-6114 Erdinç Dündar 0000-0002-0545-7486 Nimet Pancaroğlu Akın 0000-0003-2886-3679
Publication Date	March 30, 2022
Submission Date	March 26, 2021
Acceptance Date	June 1, 2021
Published in Issue	Year 2022 Volume: 71 Issue: 1

Cite

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. March 2022;71(1):1-12. doi:10.31801/cfsuasmas.903988
Chicago	Ulusu, Uğur, Erdinç Dündar, and Nimet Pancaroğlu Akın. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 1-12. https://doi.org/10.31801/cfsuasmas.903988.
EndNote	Ulusu U, Dündar E, Pancaroğlu Akın N (March 1, 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, and N. Pancaroğlu Akın, “Lacunary invariant statistical equivalence for double set sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 1–12, 2022, doi: 10.31801/cfsuasmas.903988.
ISNAD	Ulusu, Uğur et al. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 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 et al. “Lacunary Invariant Statistical Equivalence for Double Set Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 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.