Çift Küme Dizileri için β ıncı Mertebeden İnvaryant ve Lacunary İnvaryant İstatistiksel Denklik
Bu çalışmada, çift küme dizileri için Wijsman anlamında asimptotik denklik kavramına yeni bir yaklaşım olarak, çift küme dizileri için Wijsman anlamında β (0
Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences
In this study, as a new approach to the concept of asymptotical equivalence in the Wijsman sense for double set sequences, the new concepts which are called asymptotical invariant statistical equivalence of order β and asymptotical lacunary invariant statistical equivalence of order β (0
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- [1] Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Mathematische Annalen, 53, 289-321, 1900.
- [2] Mursaleen, M., Edely, O.H.H., Statistical convergence of double sequences, Journal of Mathematical Analysis and Applications, 288, 223-231, 2003.
- [3] Patterson, R.F., Savaş, E., Lacunary statistical convergence of double sequences, Mathematical Communications, 10, 55-61, 2005.
- [4] Savaş, E., Patterson, R.F., Double σ-convergence lacunary statistical sequences, Journal of Computational Analysis and Applications, 11, 610-615, 2009.
- [5] Savaş, E., Double almost statistical convergence of order α, Advances in Difference Equations, 62, 1-9, 2013.
- [6] Savaş, E., Double almost lacunary statistical convergence of order α, Advances in Difference Equations, 254, 1-10, 2013.
- [7] Patterson, R.F., Rates of convergence for double sequences, Southeast Asian Bulletin of Mathematics, 26, 469-478, 2003.
- [8] Baronti, M., Papini, P., Convergence of sequences of sets, ın: methods of functional analysis in approximation theory, Birkhäuser, Basel, 133-155, 1986.
- [9] Beer, G., Wijsman convergence: A survey, Set-Valued Analysis, 2, 77-94, 1994.
- [10] Nuray, F., Ulusu, U., Dündar, E., Lacunary statistical convergence of double sequences of sets, Soft Computing, 20, 2883-2888, 2016.
- [11] Nuray, F., Ulusu, U., Lacunary invariant statistical convergence of double sequences of sets, Creative Mathematics and Informatics, 28, 143-150, 2019.
- [12] Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iranian Journal of Mathematical Sciences and Informatics, 16, 55-64, 2021.
- [13] Nuray, F., Patterson, R.F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Mathematica, 49, 183-196, 2016.
- [14] Çolak, R., Statistical convergence of order α, In: Modern Methods in Analysis and Its Applications, Anamaya Publishers, New Delhi, 121-129, 2010.
- [15] Gülle, E., Double Wijsman asymptotically statistical equivalence of order α, Journal of Intelligent & Fuzzy Systems, 38, 2081-2087, 2020.
- [16] Pancaroğlu, N., Nuray, F., On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress in Applied Mathematics, 5, 23-29, 2013.
- [17] Pancaroğlu, N., Nuray, F., Savaş, E., On asymptotically lacunary invariant statistical equivalent set sequences, AIP Conference Proceedings, 1558, 780-781, 2013.
- [18] Savaş, E., Nuray, F., On σ-statistically convergence and lacunary σ-statistically convergence, Mathematica Slovaca, 43, 309-315, 1993.
- [19] Savaş, E., Asymptotically I-lacunary statistical equivalent of order α for sequences of sets, Journal of Nonlinear Science and its Applications, 10, 2860-2867, 2017.
- [20] Şengül, H., Et, M., On lacunary statistical convergence of order α, Acta Mathematica Scientia. Series B, 34, 473-482, 2014.
- [21] Şengül, H., On Wijsman I-lacunary statistical equivalence of order (η,μ), Journal of Inequalities and Special Functions, 9, 92-101, 2018.
- [22] Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 310438, 1-5, 2013.
- [23] Ulusu, U., Gülle, E., Some statistical convergence types of order α for double set sequences, Facta Universitatis, Series: Mathematics and Informatics, 35, 595-603, 2020.
- [24] Ulusu, U., Nuray, F., Lacunary I-invariant convergence, Cumhuriyet Science Journal, 41, 617-624, 2020.
- [25] Ulusu, U., Dündar, E., Pancaroğlu Akın, N., Lacunary invariant statistical equivalence for double set sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, (Accepted).