On Generalized ∆-statistically pre-Cauchy Triple Sequences with an Orlicz Function

  • Verda Gürdal Department of Mathematics, Süleyman Demirel University, 32260, Isparta
  • Omer Kişi Faculty of Science, Department of Mathematics, Bartın University, Bartın
Keywords: Ideal convergence, triple sequence, difference sequences, I-statistical pre-Cauchy, Orlicz function

Abstract

The primary target of this manuscript is to introduce the concept of I3-statistically convergence for difference triple sequences, and we use an Orlicz function to obtain more general results. In addition, we will present some interesting results by using ∆I3-statistically convergent sequence and ∆I3-statistically pre-Cauchy sequence via an Orlicz function.

References

Altay, B. and F. Başar (2005). Some new spaces of double sequences. Journal of Mathematical Analysis and Applications 309(1), 70–90.
Aydin, C. and F. Başar (2004). Some new difference sequence spaces. Applied Mathematics and Computation 157(3), 677–693.
Başar, F. (2012). Summability Theory and Its Applications. Bentham Science Publishers. ˙Istanbul.
Başarir, M. (1995). On the δ-statistical convergence of sequences. Firat University Turkish Journal of Science and Technology 2, 1–6.
Belen, C. and S.A. Mohiuddine (2013). Generalized weighted statistical convergence and application. Applied Mathematics and Computation 219, 9821–9826.
Connor, J., J.A. Fridy and J. Kline (1994). Statistically pre-cauchy sequences. International Journal of Control 14, 311–317.
Das, P. and E. Savas¸ (2014). On I-statistically pre-cauchy sequences. Taiwanese Journal of Mathematics 1, 115–126.
Das, P., E. Savas¸ and S.K. Ghosal (2011). On generalization sof certain summability methods using ideals. Applied Mathematics Letters 24, 1509–1514.
Demirci, I.A. and M. Gurdal (2021). On lacunary generalized statistical convergent complex uncertain triple sequence.¨ Journal of Intelligent and Fuzzy Systems 41(1), 1021–1029.
Demirci, K. (2001). I-limit superior and limit inferior. Mathematical Communications 6, 165–172.
Dutta, A.J., A. Esi and B.C. Tripathy (2013). Statistically convergence triple sequence spaces defined by Orlicz function. Journal of Mathematical Analysis 4(2), 16–22.
Esi, A. and E. Savas¸ (2015). On lacunary statistically convergent triple sequences in probabilistic normed space. Applied Mathematics and Information Sciences 9(5), 2529–2534.
Esi, A. and E. Subramanian (2017). Wijsman rough statistical convergence on triple sequences. International Journal of Sciences: Basic and Applied Research 32(3), 13–27.
Esi, A., N. Subramanian and A. Esi (2018). Wijsman rough I-convergence limit point of triple sequences defined by a metric function. Annals of Fuzzy Mathematics and Informatics 15(1), 47–57.
Et, M. and F. Nuray (2001). δm-statistical convergence. Indian Journal of Pure and Applied Mathematics 32(6), 961– 969.
Et, M. and R. C¸olak (1995). On some generalized difference sequence spaces. Soochow Journal of Mathematics 21(4), 377–386.
Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicum 2, 241–244.
Fridy, J.-A. (1985). On statistical convergence. Analysis (Munich) 5, 301–313.
Gum¨us¸, H.,O. Kisi and E. Savas¸ (2020). Some results about¨ δI-statistically pre-cauchy sequences with an orlicz function. Journal of Computational Analysis and Applications 28(1), 180–188.
Gurdal, M. (2003). Statistically pre-cauchy sequences and bounded moduli.¨ Acta et Commentationes Universitatis Tartuensis de Mathematica 7, 3–7.
Gurdal, M. and M.-B. Huban (2012). ¨I-limit points in random 2-normed spaces. Theory and Applications of Mathematics and Computer Science 2(1), 15–22.
Gurdal, V. (2021). On generalized statistical limit points for triple sequence in random 2-normed spaces.¨ Caspian Journal of Mathematical Sciences, doi. 10.22080/cjms.2021.22501.1609.
Gurdal, V. (2022). Triple sequences in the topology induced by random 2-norms.¨ Journal of Applied and Pure Mathematics, (revised version).
Huban, M.-B. (2021). Generalized statistically pre-cauchy triple sequences via orlicz functions. Journal of Nonlinear Sciences and Applications 14, 414–422.
Huban, M.-B. and M. Gurdal (2021). Wijsman lacunary invariant statistical convergence for triple sequences via Orlicz¨ function. Journal of Classical Analysis 17(2), 119–128.
Huban, M.-B., M. Gurdal and H. Bayturk (2021). On asymptotically lacunary statistical equivalent triple sequences¨ via ideals and orlicz function. Honam Mathematical Journal 43(2), 343–357.
Kadak, U. and S.A. Mohiuddine (2018). Generalized statistically almost convergence based on the difference operator which includes the (p,q)-gamma function and related approximation theorems. Results in Mathematics 73(9), 1– 31.
Khan, V.A. and Q.M.D. Lohani (2007). Statistically pre-Cauchy sequences and Orlicz functions. Southeast Asian Bulletin of Mathematics 31, 1107–1112.
Khan, V.A. and S. Tabassum (2012). Statistically pre-Cauchy double sequences. Southeast Asian Bulletin of Mathematics 36, 249–254.
Khan, V.A., K. Ebadullah and A. Ahmad (2012). I-pre-Cauchy sequences and Orlicz functions. Journal of Mathematical Analysis 3(1), 21–26.
Kişi, O., V. Gürdal and M.B. Huban (2021). Ideal statistically limit points and ideal statistically cluster points of triple¨ sequences of fuzzy numbers. Journal of Classical Analysis, in press.
Kizmaz, H. (1981). On certain sequence spaces. Canadian Mathematical Bulletin 24(2), 169–176.
Kostyrko, P., M. Macaj and T. Salat (2000a). Statistical convergence and I-convergence. http://thales.doa.fmph.uniba.sk/macaj/ICON.pdf.
Kostyrko, P., T.Salat and W. Wilezynski (2000 b). I-convergence. Real Analysis Exchange 26(2), 669–686.
Lindenstrauss, J. and L. Tzafriri (1971). On Orlicz sequence spaces. Journal of Mathematical Analysis 101, 379–390.
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 B.-A.-S. Alamri (2019). Generalization of equi-statistical convergence via weighted lacunary sequence with associated korovkin and voronovskaya type approximation theorems. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 113(3), 1955–1973.
Mursaleen, M. and F. Bas¸ar (2020). Sequence Spaces: Topics in Modern Summability Theory. CRC Press, Taylor and Francis Group, Series: Mathematics and Its Applications, Boca Raton London New York.
Nabiev, A.-A., S. Pehlivan and M. Gurdal (2007). On I-Cauchy sequences. Taiwanese Journal of Mathematics 11(2), 569–576.
Sahiner, A. and B.-C. Tripathy (2008). Some I-related properties of triple sequences. Selcuk Journal of Applied Mathematics 9(2), 9–18.
Sahiner, A., M. Gurdal and F.-K. Duden (2007). Triple sequences and their statistical convergence.¨ Selcuk Journal of Applied Mathematics 8(2), 49–55.
Yamanci, U. and M. Gurdal (2014). ¨I-statistically pre-cauchy double sequences. Global Journal of Mathematical Analysis 2(4), 297–303.
Published
2022-02-21
How to Cite
Gürdal, V., & Kişi, O. (2022). On Generalized ∆-statistically pre-Cauchy Triple Sequences with an Orlicz Function. Theory and Applications of Mathematics & Computer Science, 12(1), 1-12. Retrieved from https://www.uav.ro/applications/se/journal/index.php/TAMCS/article/view/198