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Çift Küme Dizileri için β ıncı Mertebeden İnvaryant ve Lacunary İnvaryant İstatistiksel Denklik

Year 2021, Volume 11, Issue 2, 421 - 430, 31.12.2021
https://doi.org/10.37094/adyujsci.956986

Abstract

Bu çalışmada, çift küme dizileri için Wijsman anlamında asimptotik denklik kavramına yeni bir yaklaşım olarak, çift küme dizileri için Wijsman anlamında β (0<β≤1) yıncı mertebeden asimptotik invaryant istatistiksel denklik ve asimptotik lacunary invaryant istatistiksel denklik olarak adlandırılan yeni kavramlar tanıtıldı ve örneklerle açıklandı. Ayrıca, bu kavramlar arasında bazı ilişkilerin varlığı ve dahası bu kavramlar ve daha önceden çift küme dizileri için Wijsman anlamında çalışılmış asimptotik denklik kavramları arasındaki ilişkiler incelendi.   

References

  • [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).

Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences

Year 2021, Volume 11, Issue 2, 421 - 430, 31.12.2021
https://doi.org/10.37094/adyujsci.956986

Abstract

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<β≤1) in the Wijsman sense for double set sequences are introduced and explained with examples. In addition, the existence of some relations between these concepts and furthermore, the relationships between these concepts and previously studied asymptotical equivalence concepts in the Wijsman sense for double set sequences are investigated.

References

  • [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).

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Uğur ULUSU (Primary Author)
SİVAS CUMHURİYET UNIVERSITY
0000-0001-7658-6114
Türkiye


Erdinç DÜNDAR
AFYON KOCATEPE UNIVERSITY
0000-0002-0545-7486
Türkiye


Fatih NURAY
AFYON KOCATEPE UNIVERSITY
0000-0003-0160-4001
Türkiye

Publication Date December 31, 2021
Application Date June 24, 2021
Acceptance Date November 24, 2021
Published in Issue Year 2021, Volume 11, Issue 2

Cite

Bibtex @research article { adyujsci956986, journal = {Adıyaman University Journal of Science}, issn = {2147-1630}, eissn = {2146-586X}, address = {}, publisher = {Adıyaman University}, year = {2021}, volume = {11}, number = {2}, pages = {421 - 430}, doi = {10.37094/adyujsci.956986}, title = {Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences}, key = {cite}, author = {Ulusu, Uğur and Dündar, Erdinç and Nuray, Fatih} }
APA Ulusu, U. , Dündar, E. & Nuray, F. (2021). Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences . Adıyaman University Journal of Science , 11 (2) , 421-430 . DOI: 10.37094/adyujsci.956986
MLA Ulusu, U. , Dündar, E. , Nuray, F. "Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences" . Adıyaman University Journal of Science 11 (2021 ): 421-430 <https://dergipark.org.tr/en/pub/adyujsci/issue/67254/956986>
Chicago Ulusu, U. , Dündar, E. , Nuray, F. "Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences". Adıyaman University Journal of Science 11 (2021 ): 421-430
RIS TY - JOUR T1 - Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences AU - Uğur Ulusu , Erdinç Dündar , Fatih Nuray Y1 - 2021 PY - 2021 N1 - doi: 10.37094/adyujsci.956986 DO - 10.37094/adyujsci.956986 T2 - Adıyaman University Journal of Science JF - Journal JO - JOR SP - 421 EP - 430 VL - 11 IS - 2 SN - 2147-1630-2146-586X M3 - doi: 10.37094/adyujsci.956986 UR - https://doi.org/10.37094/adyujsci.956986 Y2 - 2021 ER -
EndNote %0 Adıyaman University Journal of Science Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences %A Uğur Ulusu , Erdinç Dündar , Fatih Nuray %T Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences %D 2021 %J Adıyaman University Journal of Science %P 2147-1630-2146-586X %V 11 %N 2 %R doi: 10.37094/adyujsci.956986 %U 10.37094/adyujsci.956986
ISNAD Ulusu, Uğur , Dündar, Erdinç , Nuray, Fatih . "Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences". Adıyaman University Journal of Science 11 / 2 (December 2021): 421-430 . https://doi.org/10.37094/adyujsci.956986
AMA Ulusu U. , Dündar E. , Nuray F. Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences. ADYU J SCI. 2021; 11(2): 421-430.
Vancouver Ulusu U. , Dündar E. , Nuray F. Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences. Adıyaman University Journal of Science. 2021; 11(2): 421-430.
IEEE U. Ulusu , E. Dündar and F. Nuray , "Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences", Adıyaman University Journal of Science, vol. 11, no. 2, pp. 421-430, Dec. 2021, doi:10.37094/adyujsci.956986

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