Deferred d-Statistical Boundedness of Order α in Metric Spaces
DOI:
https://doi.org/10.56405/dngcrj.2024.09.01.01Keywords:
Deferred statistical convergence, statistical boundedness, metric spaceAbstract
In this study, we introduce the concept of deferred d−statistically bounded sequences of order \alpha and give some relations betwen deferred d−statistically bounded sequences of order \alpha and deferred d−strongly p−Ces`aro summable sequences of order α in a general metric space.
Downloads
References
Akbaş, K.E., & Işık, M. (2020). On asymptotically λ-statistical equivalent sequences of order α in probability. Filomat, 34 (13), 4359-4365.
Agnew, R.P. (1932). On deferred Cesàro means. Annals of Mathematics, 33(3), 413-421.
Alotaib, A. & Mursaleen, M. (2014). Statistical convergence in random paranormed space. Journal of Computational Analysis and Applications, 17 (2), 297-304.
Bal, P., & Rakshit, D. (2023). A Variation of the Class of Statistical γ-Covers. Topological Algebra and its Applications, 11 (1), 20230101.
Bhardwaj, V.K., & Bala, I. (2007). On Weak Statistical Convergence. International Journal of Mathematics and Mathematical Sciences, Article ID 38530, 9 pages.
Bilalov, B., & Nazarova, T.Y. (2015a). On Statistical Convergence in Metric Space. Journal of Mathematics Research, 7 (1), 37-43.
Bilalov, B., & Nazarova, T.Y. (2015b). Statistical convergence of functional sequences. Rocky Mountain Journal of Mathematics, 45 (5), 1413-1423.
Bilalov, B., & Nazarova, T.Y. (2016). On statistical type convergence in uniform spaces. Bulletin of Iranian Mathematical Society, 42 (4), 975-986.
Bilalov, B., & Sadigova, S.R. (2015). On μ-statistical convergence. Proceedings of the American Mathematical Society, 143 (9), 3869-3878.
Çakallı, H. (1995). Lacunary Statistical Convergence in Topological Groups. Indian Journal of Pure and Applied Mathematics, 26 (2), 113-119.
Çakallı, H., Aras, C.G., & Sönmez, A. (2015). Lacunary Statistical Ward Continuity. AIP Conference Proceedings, 1676, 020042. DOI: http://dx.doi.org/10.1063/1.4930468.
Çakallı, H., & Kaplan, H. (2017). A Variation on Lacunary Statistical Quasi Cauchy Sequences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 66 (2), 71-79.
Çakallı, H. (2019). A New Approach to Statistically Quasi Cauchy Sequences. Maltepe Journal of Mathematics, 1 (1), 1-8.
Caserta, A., Maio, G.Di., & Koçinac, L.D.R. (2011). Statistical Convergence in Function Spaces. Abstract and Applied Analysis, Article ID 420419, 11 pages.
Çınar, M, Karakas, M., Et, M. (2013). On Pointwise and Uniform Statistical Convergence of Order α for Sequences of Functions. Fixed Point Theory And Applications, 2013, 33.
Çolak, R. (2010). Statistical Convergence of Order α. Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Publication, 2010, 121-129.
Connor, J.S. (1988). The Statistical and Strong p-Cesàro Convergence of Sequences. Analysis, 8, 47-63.
Et, M., Çolak, R., & Altın, Y. (2014). Strongly Almost Summable Sequences of Order α. Kuwait Journal of Sciences, 41 (2), 35-47.
Et, M., Altınok, H., & Çolak, R. (2006). On λ-Statistical Convergence of Difference Sequences of Fuzzy Numbers. Information Sciences, 176 (15), 2268-2278.
Et, M., Mohiuddine, S.A., Şengül, H. (2016). On Lacunary Statistical Boundedness of Order α. Facta Universitatis. Series: Mathematics and Informatics, 31 (3), 707-716.
Et, M., Karatas, M. (2019). On Lacunary d-Statistical Convergence of Order α. AIP Conference Proceedings, 2086, 030017. DOI: https://doi.org/10.1063/1.5095102.
Et, M., Cınar, M., Şengül, H. (2019). Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science andTechnology, 2 (3), 189-193.
Et, M., Cınar, M., Kandemir, H.Ş. (2020). Deferred statistical convergence of order α in metric spaces. AIMS Mathematics, 5 (4), 3731-3740.
Maio, G. Di., Koçinac, L.D.R. (2008). Statistical Convergence in Topology. Topology and its Applications, 156, 28-45.
Fast, H. (1951). Sur la Convergence Statistique. Colloquium Mathematicae, 2, 241-244.
Fridy, J. (1985). On Statistical Convergence, Analysis, 5, 301-313.
Fridy, J., & Orhan, C. (1993). Lacunary Statistical Convergence. Pacific Journal of Mathematics, 160, 43-51.
Fridy, J., & Orhan, C. (1997). Statistical Limit Superior and Limit Inferior. Proceedings of the American Mathematical Society, 125 (12), 3625-3631.
Işık, M., Akbaş, K.E. (2017a). On λ-statistical convergence of order α in probability. Journal of Inequalities and Special Functions, 8 (4), 57-64.
Işık, M., Akbaş, K.E. (2017b). On asymtotically lacunary statistical equivalent sequences of order α in probability. ITM Web of Conferences 13, 01024. DOI: 10.1051/itmconf/20171301024.
Işık, M., Et, K.E. (2015). On lacunary statistical convergence of order α in probability. AIP Conference Proceedings 1676, 020045. DOI: http://dx.doi.org/10.1063/1.4930471.
Kayan, E., Çolak, R., Altın, Y. (2018). d-Statistical Convergence of Order α and d-Statistical Boundedness of Order α in Metric Spaces. Politehnica University of Bucharest Scientific Bulletin Series A: Applied Mathematics and Physics, 80 (4), 229-238.
Küçükaslan, M., Değer, U. & Dovgoshey, O. (2014). On The Statistical Convergence of Metric-Valued Sequences. Ukrainian Mathematical Journal, 66 (5), 796-805.
Küçükaslan, M., Değer, U. (2012). On Statistical Boundedness of Metric Valued Sequences. European Journal of Pure and Applied Mathematics, 5 (2), 174-186.
Mursaleen, M. (2012). λ-Statistical Convergence. Mathematica Slovaca, 50 (1), 111-115.
Salat, T. (1980). On Statistically Convergent Sequences of Real Numbers. Mathematica Slovaca, 30, 139-150.
Savas, E. (2006). Generalized Asymptotically I-Lacunary Statistical Equivalent of Order α for Sequences of Sets. Filomat, 31 (6), 1507-1514.
Schoenberg, I.J. (1959). The Integrability of Certain Functions and Related Summability Methods. American Mathematical Monthly, 66, 361-375.
Şengül, H. (2017). Some Cesàro-type Summability Spaces Defined by a Modulus Function of Order (α,β). Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 66 (2), 80-90.
Şengül, H. (2017). On S_α^β (θ)-Convergence and Strong N_α^β (θ,p)-Summability. Journal of Nonlinear Science and Application, 10 (9), 5108-5115.
Şengül, H., & Et, M. (2017). On I-Lacunary Statistical Convergence of Order α of Sequences of Sets. Filomat, 31 (8), 2403-2412.
Şengül, H., Et, M., Çakallı, H. (2019). Lacunary d-Statistical Convergence and Lacunary d-Statistical Boundedness in Metric Spaces. International Conference ofMathematical Sciences, (ICMS 2019), Maltepe University, Istanbul, Turkey.
Steinhaus, H. (1951). Sur la Convergence Ordinaire et la Convergence Asymptotique. Colloquium Mathematicae, 2, 73-74.
Zygmund, A. (1979). Trigonometric Series. Cambridge University Press, Cambridge, UK.
Downloads
Published
How to Cite
Issue
Section
License
Dera Natung Government College Research Journal retains the copyright of the article and its contents. The authors are expected to obtain permission from the journal if they choose to reuse the article under Creative Commons Attribution 4.0 International License (CC BY 4.0). Upon having received the journal’s permission, this open license would allow the authors for reuse or adaptation as long as their original article is properly and adequately cited.