پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 696 |
| تعداد مقالات | 10,085 |
| تعداد مشاهده مقاله | 71,166,717 |
| تعداد دریافت فایل اصل مقاله | 62,896,813 |
New results on $ f $-statistical convergence of order $ \tilde{\alpha} $ through triple sequences spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 17، شماره 3، خرداد 2026، صفحه 15-24 اصل مقاله (395.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25758.3119 | ||
| نویسندگان | ||
| Carlos Granados* 1؛ Omer Kisi2 | ||
| 1Escuela Ciencias de la Educacion, Universidad Nacional Abierta y a Distancia, Barranquilla, Colombia | ||
| 2Department of Mathematics, Faculty of Sciences, Bartin University, 74100 Bartin, Turkey | ||
| تاریخ دریافت: 10 دی 1400، تاریخ بازنگری: 06 خرداد 1401، تاریخ پذیرش: 21 خرداد 1401 | ||
| چکیده | ||
| In this paper, we define new notions of $ f $-statistical convergence for triple sequences of order $ \tilde{\alpha}$ and strong $ f $-Cesaro summability for triple sequences of order $ \tilde{\alpha} $. Moreover we show the relationship between the spaces $ w_{\tilde{\alpha},0}^{3}(f) $, $ w_{\tilde{\alpha}}^{3}(f) $ and $ w_{\tilde{\alpha},\infty}^{3}(f) $. Additionally, we show some properties of the strong $ f $-Cesaro summability of order $ \tilde{\beta} $. The main purpose of this paper is to examine the concept of $f$-triple statistical convergence of order $\alpha $; where $f$-is an unbounded function and give relations between $f$-triple statistical convergence of order $\alpha $ and strong $f$-Ces\`aro summability for a triple sequence of order $\alpha $. | ||
| کلیدواژهها | ||
| Triple sequences؛ statistical convergence؛ Ces\`aro summability method | ||
| مراجع | ||
|
[1] A. Aizpuru, M. C. Listan-Garcia, and F. Rambla-Barreno, Density by moduli and statistical convergence, Quaest. Math. 37 (2014), no. 4, 525–530. [2] V.K. Bhardwaj and S. Dhawan, f-statistical convergence of order α and strong Cesaro summability of order α˜ with respect to a modulus, J. Inequal. Appl. 332 (2015), 14. [3] J.S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988), no. 2, 47–63. [4] R. C¸ olak and Y. Altin, Statistical convergence of double sequences of order α˜, J. Funct. Spaces Appl. 5 (2012), 682823. [5] R. Colak, Statistical convergence of order a, M. Mursaleen, Modern methods in analysis and its applications, Anamaya Pub., New Delhi, 2010, pp. 121–129. [6] I.A. Demirci and M. Gurdal, Lacunary statistical convergence for sets of triple sequences via Orlicz function, Theory Appl. Math. Comput. Sci. 11 (2021), no. 1, 1–13. [7] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. [8] J.A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313. [9] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mt. J. Math. 32 (2002), no. 1, 129–138. [10] C. Granados, A generalization of the strongly Cesaro ideal convergence through double sequence spaces, Int. J. Appl. Math. 34 (2021), no. 3, 525–533. [11] C. Granados, New notions of triple sequences on ideal spaces in metric spaces, Adv. Theory Nonlinear Anal. Appl. 5 (2021), no. 3, 363–368. [12] C. Granados, Statistical convergence of double sequences in neutrosophic normed spaces, Neutrosophic Sets Syst. 42 (2021), 333–344. [13] C. Granados and A.K. Das, A generalization of triple statistical convergence in topological groups, Int. J. Appl. Math. 35 (2022), no. 1, 57–62. [14] C. Granados and A.K. Das, New Tauberian theorems for statistical Ces`aro summability of function of three variables over a locally convex space, Armen. J. Math. 14 (2022), no. 5, 1–15 [15] C. Granados and B.O. Osu, Wijsman and Wijsman regularly triple ideal convergence sequences of sets, Sci. Afr. 15 (2022), e01101. [16] C. Granados, A generalized of Sλ-I-convergence of complex uncertain double sequences, Ingen. Cien. 17 (2021), no. 34, 53–75. [17] C. Granados, Convergencia estadistica en medida para sucesiones triples de funciones con valores difusos, Rev. Acad. Colombiana Cien. Exactas Fis. Natur. 45 (2021), no. 177, 1011–1021. [18] C. Granados and J. Bermudez, I2-localized double sequences in metric spaces, Adv. Math.: Sci. J. 10 (2021), no. 6, 2877–2885. [19] C. Granados, A.K. Das, and B.O. Osu, Mλm,n,p-statistical convergence for triple sequences, J. Anal. 29 (2021), no. 4, 1–18 [20] M. B. Huban, M. Gu rdal, and H. Bayturk, On asymptotically lacunary statistical equivalent triple sequences via ideals and Orlicz function, Honam Math. J. 43 (2021), no. 2, 343–357. [21] I.J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Camb. Philos. Soc. 104 (1988), no. 1, 141–145. [22] I.J. Maddox, Inclusions between FK-spaces and Kuttner’s theorem, Math. Proc. Camb. Philos. Soc. 101 (1987), no. 3, 523–527. [23] I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc. 100 (1986), 161–166. [24] H. Nakano, Concave modulars, J. Math. Soc. Jpn. 5 (1953), 29–49. [25] A. Pringsheim, Zur Ttheorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321. [26] E. Rodriguez, C. Granados, and J. Bermudez, A generalized of N¨orlund ideal convergent double sequence spaces, WSEAS Trans. Math. 20 (2021), 562–568. [27] A. Sahiner, M. Gurdal, and F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. 8 (2007), no. 2, 49–55. [28] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. [29] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. [30] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74. [31] B. Torgut and Y. Altin, f-statistical convergence of double sequences of order α˜, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90 (2020), 803–808. [32] B.C. Tripathy and B. Sarma B, Statistically convergent difference double sequence spaces, Acta. Math. Sin (Engl. Ser.) 24 (2008), no. 5, 737–742. [33] B.C. Tripathy, Statistically convergent double sequences. Tamkang J. Math. 34 (2003), no. 3, 231–237. [34] B.C. Tripathy and B. Sarma, Vector valued paranormed statistically convergent double sequence spaces, Math. Slovaca 57 (2007), no. 2, 179–188. [35] B.C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Math. Slovaca 59 (2009), no. 6, 767–776. [36] B.C. Tripathy and R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Jour. Math. 33 (2014), no. 2, 157-174. [37] B.C. Tripathy and R. Goswami, Vector valued multiple sequences defined by Orlicz functions, Bol. Soc. Paranaense Mate. 33 (2015), no. 1, 67–79. [38] B.C. Tripathy and R. Goswami, Multiple sequences in probabilistic normed spaces, Afr. Mate. 26 (2015), no. 5-6, 753-760. [39] B.C. Tripathy and R. Goswami, Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces, Afr. Mate. 26 (2015), no. 7-8, 1281–1289. [40] B.C. Tripathy and R. Goswami, Statistically convergent multiple sequences in probabilistic normed spaces, U.P.B. Sci. Bull., Ser. A, 78 (2016), no. 4, 83–94. [41] A. Zygmund, Trigonometric Series, vol I, II. Cambridge University Press, Cambridge, 1997. | ||
|
آمار تعداد مشاهده مقاله: 833 تعداد دریافت فایل اصل مقاله: 419 |
||