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Wijsman asymptotical I_2-statistically equivalent double set sequences of order η

Year 2020, Volume: 69 Issue: 1, 854 - 862, 30.06.2020
https://doi.org/10.31801/cfsuasmas.695309

Abstract

In this study, we present notions of Wijsman asymptotical I₂-statistically equivalence of order η, Wijsman asymptotical I₂-Cesàro equivalence of order η and Wijsman asymptotical strongly p-I₂-Cesàro equivalence of order η for double set sequences where 0<η≤1. Also, we investigate some properties of these notions and some relationships between them.

References

  • Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289--321.
  • Mursaleen, M., Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223--231.
  • Das, P., Kostyrko, P., Wilczyński, W., Malik, P., I and I^{∗}-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605--620.
  • Bhunia, S., Das, P., Pal, S.K., Restricting statistical convergence, Acta Mathematica Hungarica, 134(1-2) (2012), 153--161
  • Çolak, R., Altın, Y., Statistical convergence of double sequences of order α, Journal of Function Spaces and Applications, 2013(Article ID 682823) (2013), 5 pages.
  • Savaş, E., Double almost statistical convergence of order α, Advances in Difference Equations, 2013(62) (2013), 9 pages.
  • Altın, Y., Çolak, R., Torgut, B., I₂(u)-convergence of double sequences of order (α,β), Georgian Mathematical Journal, 22(2) (2015), 153--158.
  • Patterson, R.F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2002), 469--478.
  • Kavita, K., Sharma, A., Kumar, V., On generelized asymptotically equivalent double sequences through (V,λ,μ)-summability, Acta Universitatis Matthiae Belii, series Mathematics, 2013 (2013), 9 pages.
  • Hazarika, B., Kumar, V., On asymptotically double lacunary statistical equivalent sequences in ideal context, Journal of Inequalities and Applications, 2013(543) (2013), 15 pages.
  • Esi, A., Açıkgöz, M., On λ₂-asymptotically double statistical equivalent sequences, Int. J. Nonlinear Anal. Appl., 5(2) (2014), 16--21.
  • Baronti, M., Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133--155), Birkhäuser, Basel, 1986.
  • Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2 (1994), 77--94.
  • Wijsman, R.A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70 (1964), 186--188.
  • Nuray, F., Ulusu, U., Dündar, E., Cesàro summability of double sequences of sets, Gen. Math. Notes, 25(1) (2014), 8--18.
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman I₂-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2 (2014) 35--39.
  • Dündar, E., Ulusu, U., Aydın, B., I₂-lacunary statistical convergence of double sequences of sets, Konuralp Journal of Mathematics, 5(1) (2017), 1--10.
  • Ulusu, U., Dündar, E., Gülle, E., I₂-Cesàro summability of double sequences of sets, Palestine Journal of Mathematics, 9(1) (2020), 561--568.
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., (in press).
  • Ulusu, U., Gülle, E., Some statistical convergence types for double set sequences of order α, Facta Univ. Ser. Math. Inform., (in press).
  • Nuray, F., Patterson, R.F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Mathematica, 49(2) (2016), 183--196.
  • Ulusu, U., Dündar, E., Asymptotically I₂-lacunary statistical equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(2) (2016), 44--56.
  • Ulusu, U., Dündar, E., Aydın, B., Asymptotically I₂-Cesàro equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(4) (2016), 225--234.
  • Gülle, E., Double Wijsman asymptotically statistical equivalence of order α, Journal of Intelligent and Fuzzy Systems, 38(2) (2020), 2081--2087.
  • Kostyrko, P., Šalát, T., Wilczyński, W., I-convergence, Real Anal. Exchange, 26(2) (2000), 669--686.
  • Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 2013(Article ID 310438) (2013), 5 pages.
  • Kişi, Ö., Nuray, F., On S_{λ}(I)-asymptotically statistical equivalence of sequence of sets, ISRN Mathematical Analysis, 2013(Article ID 602963) (2013), 6 pages.
  • Das, P., Savaş, E., On I-statistical and I-lacunary statistical convergence of order α, Bull. Iranian Math. Soc., 40(2) (2014), 459--472.
  • Et, M. and Şengül, H., Some Cesàro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8) (2014), 1593--1602.
  • Sever, Y., Ulusu, U., Dündar, E., On strongly I and I^{∗}-lacunary convergence of sequences of sets, AIP Conference Proceedings, 2014(1611) (2014), 357--362.
  • Ulusu, U., Dündar, E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567--1574.
  • Savaş, E., On I-lacunary statistical convergence of order α for sequences of sets, Filomat, 29(6) (2015), 1223--1229.
  • Savaş, E., Asymptotically I-lacunary statistical equivalent of order α for sequences of sets, Journal of Nonlinear Sciences and Applications, 10 (2017), 2860--2867.
  • Şengül, H. and Et, M., On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8) (2017), 2403--2412.
  • Şengül, H., On Wijsman I-lacunary statistical equivalence of order (η,μ), Journal of Inequalities and Special Functions, 9(2) (2018), 92--101.
Year 2020, Volume: 69 Issue: 1, 854 - 862, 30.06.2020
https://doi.org/10.31801/cfsuasmas.695309

Abstract

References

  • Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289--321.
  • Mursaleen, M., Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223--231.
  • Das, P., Kostyrko, P., Wilczyński, W., Malik, P., I and I^{∗}-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605--620.
  • Bhunia, S., Das, P., Pal, S.K., Restricting statistical convergence, Acta Mathematica Hungarica, 134(1-2) (2012), 153--161
  • Çolak, R., Altın, Y., Statistical convergence of double sequences of order α, Journal of Function Spaces and Applications, 2013(Article ID 682823) (2013), 5 pages.
  • Savaş, E., Double almost statistical convergence of order α, Advances in Difference Equations, 2013(62) (2013), 9 pages.
  • Altın, Y., Çolak, R., Torgut, B., I₂(u)-convergence of double sequences of order (α,β), Georgian Mathematical Journal, 22(2) (2015), 153--158.
  • Patterson, R.F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2002), 469--478.
  • Kavita, K., Sharma, A., Kumar, V., On generelized asymptotically equivalent double sequences through (V,λ,μ)-summability, Acta Universitatis Matthiae Belii, series Mathematics, 2013 (2013), 9 pages.
  • Hazarika, B., Kumar, V., On asymptotically double lacunary statistical equivalent sequences in ideal context, Journal of Inequalities and Applications, 2013(543) (2013), 15 pages.
  • Esi, A., Açıkgöz, M., On λ₂-asymptotically double statistical equivalent sequences, Int. J. Nonlinear Anal. Appl., 5(2) (2014), 16--21.
  • Baronti, M., Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133--155), Birkhäuser, Basel, 1986.
  • Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2 (1994), 77--94.
  • Wijsman, R.A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70 (1964), 186--188.
  • Nuray, F., Ulusu, U., Dündar, E., Cesàro summability of double sequences of sets, Gen. Math. Notes, 25(1) (2014), 8--18.
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman I₂-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2 (2014) 35--39.
  • Dündar, E., Ulusu, U., Aydın, B., I₂-lacunary statistical convergence of double sequences of sets, Konuralp Journal of Mathematics, 5(1) (2017), 1--10.
  • Ulusu, U., Dündar, E., Gülle, E., I₂-Cesàro summability of double sequences of sets, Palestine Journal of Mathematics, 9(1) (2020), 561--568.
  • Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., (in press).
  • Ulusu, U., Gülle, E., Some statistical convergence types for double set sequences of order α, Facta Univ. Ser. Math. Inform., (in press).
  • Nuray, F., Patterson, R.F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Mathematica, 49(2) (2016), 183--196.
  • Ulusu, U., Dündar, E., Asymptotically I₂-lacunary statistical equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(2) (2016), 44--56.
  • Ulusu, U., Dündar, E., Aydın, B., Asymptotically I₂-Cesàro equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(4) (2016), 225--234.
  • Gülle, E., Double Wijsman asymptotically statistical equivalence of order α, Journal of Intelligent and Fuzzy Systems, 38(2) (2020), 2081--2087.
  • Kostyrko, P., Šalát, T., Wilczyński, W., I-convergence, Real Anal. Exchange, 26(2) (2000), 669--686.
  • Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 2013(Article ID 310438) (2013), 5 pages.
  • Kişi, Ö., Nuray, F., On S_{λ}(I)-asymptotically statistical equivalence of sequence of sets, ISRN Mathematical Analysis, 2013(Article ID 602963) (2013), 6 pages.
  • Das, P., Savaş, E., On I-statistical and I-lacunary statistical convergence of order α, Bull. Iranian Math. Soc., 40(2) (2014), 459--472.
  • Et, M. and Şengül, H., Some Cesàro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8) (2014), 1593--1602.
  • Sever, Y., Ulusu, U., Dündar, E., On strongly I and I^{∗}-lacunary convergence of sequences of sets, AIP Conference Proceedings, 2014(1611) (2014), 357--362.
  • Ulusu, U., Dündar, E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567--1574.
  • Savaş, E., On I-lacunary statistical convergence of order α for sequences of sets, Filomat, 29(6) (2015), 1223--1229.
  • Savaş, E., Asymptotically I-lacunary statistical equivalent of order α for sequences of sets, Journal of Nonlinear Sciences and Applications, 10 (2017), 2860--2867.
  • Şengül, H. and Et, M., On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8) (2017), 2403--2412.
  • Şengül, H., On Wijsman I-lacunary statistical equivalence of order (η,μ), Journal of Inequalities and Special Functions, 9(2) (2018), 92--101.
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Uğur Ulusu 0000-0001-7658-6114

Esra Gülle 0000-0001-5575-2937

Publication Date June 30, 2020
Submission Date February 27, 2020
Acceptance Date April 24, 2020
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Ulusu, U., & Gülle, E. (2020). Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 854-862. https://doi.org/10.31801/cfsuasmas.695309
AMA Ulusu U, Gülle E. Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):854-862. doi:10.31801/cfsuasmas.695309
Chicago Ulusu, Uğur, and Esra Gülle. “Wijsman Asymptotical I_2-Statistically Equivalent Double Set Sequences of Order η”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 854-62. https://doi.org/10.31801/cfsuasmas.695309.
EndNote Ulusu U, Gülle E (June 1, 2020) Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 854–862.
IEEE U. Ulusu and E. Gülle, “Wijsman asymptotical I_2-statistically equivalent double set sequences of order η”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 854–862, 2020, doi: 10.31801/cfsuasmas.695309.
ISNAD Ulusu, Uğur - Gülle, Esra. “Wijsman Asymptotical I_2-Statistically Equivalent Double Set Sequences of Order η”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 854-862. https://doi.org/10.31801/cfsuasmas.695309.
JAMA Ulusu U, Gülle E. Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:854–862.
MLA Ulusu, Uğur and Esra Gülle. “Wijsman Asymptotical I_2-Statistically Equivalent Double Set Sequences of Order η”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 854-62, doi:10.31801/cfsuasmas.695309.
Vancouver Ulusu U, Gülle E. Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):854-62.

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

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