Deferred statistical convergence of double sequences in neutrosophic normed spaces

The Journal of Analysis - Trang 1-22 - 2023
Ömer Kişi1, Chiranjib Choudhury2
1Department of Mathematics, Bartın University, Bartin, Turkey
2Department of Mathematics, Tripura University (A Central University), Suryamaninagar, India

Tóm tắt

This work explores the concepts of deferred Cesàro mean and deferred statistical convergence for double sequences in neutrosophic normed spaces (shortly NNS). We investigate several fundamental properties of these newly studied concepts. Additionally, we introduce the notion of deferred statistical Cauchy sequences and establish the equivalence between deferred statistical convergent double sequences and deferred statistical Cauchy double sequences in NNS.

Tài liệu tham khảo

Agnew, R.P. 1932. On deferred Cesàro mean. Annals of Mathematics 33 (3): 413–421. Altinok, M., M. Küçükaslan, and U. Kaya. 2021. Statistical extension of bounded sequence space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 (1): 82–99. Atanassov, K.T. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1): 87–96. Belen, C., and S.A. Mohiuddine. 2013. Generalized weighted statistical convergence and application. Applied Mathematics and Computation 219 (18): 9821–9826. Dağadur, I., and Ş Sezgek. 2016. Deferred Cesàro mean and deferred statistical convergence of double sequences. Journal of Inequalities and Special Functions 7 (4): 118–136. Datta, D., and B.C. Tripathy. 2022. Statistical convergence of double sequences of complex uncertain variables. Journal of Applied Mathematics & Informatics 40 (1–2): 191–204. Datta, D., and B.C. Tripathy. 2020. Convergence of complex uncertain double sequences. New Mathematics and Natural Computation 16 (3): 447–459. Debnath, S., S. Debnath, and C. Choudhury. 2022. On deferred statistical convergence of sequences in neutrosophic normed spaces. Sahand Communications in Mathematical Analysis 19 (4): 81–96. Et, M., M. Çinar, and H. Şengül. 2019. On ∆m-asymptotically deferred statistical equivalent sequences of order α. Filomat 33 (7): 1999–2007. Et, M., and H. Şengül. 2014. Some Cesàro-type summability spaces of order α and lacunary statistical convergence of order α. Filomat 28 (8): 1593–1602. Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum 2: 241–244. Felbin, C. 1992. Finite dimensional fuzzy normed linear space. Fuzzy Sets and Systems 48 (2): 239–248. Freedman, A.R., and J.J. Sember. 1981. Densities and summability. Pacific Journal of Mathematics 95 (2): 293–305. Fridy, J.A. 1985. On statistical convergence. Analysis 5 (4): 301–313. Kadak, U., and S.A. Mohiuddine. 2018. On generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems space. Results in Mathematics 73 (9): 1–31. Karakuş, S., K. Demirci, and O. Duman. 2008. Statistical convergence on intuitionistic fuzzy normed spaces. Chaos, Solitons & Fractals 35 (4): 763–769. Khan, V.A., H. Fatima, M.D. Khan, and A. Ahamd. 2021. Spaces of neutrosophic λ-statistical convergence sequences and their properties. Journal of Mathematics and Computer Science 23 (1): 1–9. Khan, V.A., M.D. Khan, and A. Ahamd. 2021. Some new type of lacunary statistically convergent sequences in neutrosophic normed space. Neutrosophic Sets and Systems 42 (14): 240–252. Khan, V.A., M.D. Khan, and A. Ahamd. 2021. Some results of neutrosophic normed spaces via Fibonacci matrix. UPB Scientific Bulletin, Series A 83 (2): 99–110. Kirişci, M., and N. Şimşek. 2020. Neutrosophic normed space and statistical convergence. The Journal of Analysis 28 (4): 1059–1073. Kişi, Ö. 2021. Convergence methods for double sequences and applications in neutrosophic normed spaces. In Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences, 137–153. Boca Raton, London, New York: CRC Press/Taylor & Francis Group. Küçükaslan, M., and M. Yılmaztürk. 2016. On deferred statistical convergence of sequences. Kyungpook Mathematical Journal 56: 357–366. Lael, F., and K. Nourouzi. 2008. Some results on the IF-normed spaces. Chaos, Solitons & Fractals 37: 931–939. Melliani, S., M. Küçükaslan, H. Sadiki, and L.S. Chadli. 2018. Deferred statistical convergence of sequences in intuitionistic fuzzy normed spaces. Notes on Intuitionistic Fuzzy Sets 24 (3): 64–78. Menger, K. 1942. Statistical metrics. Proceedings of the National Academy of Sciences of the United States of America 28 (12): 535–537. Mohiuddine, S.A., A. Asiri, and B. Hazarika. 2019. Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems. International Journal of General Systems 48 (5): 492–506. Mohiuddine, S.A., and Q.M. Danish Lohani. 2009. On generalized statistical convergence in intuitionistic fuzzy normed space. Chaos, Solitons & Fractals 42 (3): 1731–1737. Mursaleen, M., and O.H.H. Edely. 2003. Statistical convergence of double sequences. Journal of Mathematical Analysis and Applications 288: 223–231. Mursaleen, M., and S.A. Mohiuddine. 2009. Statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Chaos, Solitons & Fractals 41 (5): 2414–2421. Nayak, L., B.C. Tripathy, and P. Baliarsingh. 2019. On deferred-statistical convergence of uncertain sequences. International Journal of General Systems 51 (6): 631–647. Şengül, H., M. Et, and M. Çınar. 2019. On I-deferred statistical convergence of order α. Filomat 33 (9): 2833–2840. Smarandache, F. 2005. Neutrosophic set a generalization of the intuitionistic fuzzy sets. International Journal of Pure and Applied Mathematics 24 (3): 287–297. Temizsu, F., M. Et, and M. Çınar. 2016. Δm-deferred statistical convergence of order α. Filomat 30 (3): 667–673. Tripathy, B.C. 2003. Statistically convergent double sequences. Tamkang Journal of Mathematics 34: 230–237. Tripathy, B.C., and M. Sen. 2001. On generalized statistically convergent sequences. Indian Journal of Pure and Applied Mathematics 32 (11): 1689–1694. Yilmaztürk, M., and M. Küçükaslan. 2013. On strongly deferred Cesàro summability and deferred statistical convergence of the sequences. Bitlis Eren University Journal of Science and Technology 3 (1): 22–25. Zadeh, L.A. 1965. Fuzzy sets. Information and Control 8 (3): 338–353.