Some Properties of Rough Statistical Convergence in 2-Normed Spaces

Abstract

In this study, we introduce the concepts of rough statistical cluster point and rough statistical limit point of a sequence in 2-normed space and investigate some properties of these concepts.

Keywords

• Rough convergence
• 2-normed space
• Rough cluster point
• Rough limit point
• Statistical convergence

References

1. 1 M. Arslan, E. Dündar, I-Convergence and I-Cauchy Sequence of Functions In 2-Normed Spaces, Konuralp J. Math. 6(1) (2018) 57–62.
2. 2 M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math. 42 (2018), 491–502.
3. 3 M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl. 10(3) (2018), 1–9.
4. 4 M. Arslan, E. Dündar, On Rough Convergence in 2-Normed Spaces and Some Properties, Filomat 33(16) (2019), 5077–5086.
5. 5 M. Arslan, E. Dündar, Rough Statistical Convergence in 2-Normed Spaces, J. Appl. Math. Inform. (in review).
6. 6 S. Aytar, Rough statistical convergence,Numer. Funct. Anal. Optim. 29(3-4): (2008), 291–303.
7. 7 S. Aytar, The rough limit set and the core of a real requence, Numer. Funct. Anal. Optim. 29(3-4): (2008), 283–290.
8. 8 S. Aytar, Rough statistical cluster points, Filomat 31(16): (2017), 5295–5304.

9. 9 H. Çakallı and S. Ersan, New types of continuity in 2-normed spaces, Filomat 30(3) (2016), 525–532.
10. 10 P. Das, S. Ghosal, A. Ghosh, Rough statistical convergence of a sequence of random variables in probability, Afrika Mat. 26(2015) 1399–1412.
11. 11 E. Dündar, C. Çakan, Rough I-convergence, Gulf J. Math. 2(1) (2014), 45–51.
12. 12 E. Dündar, C. Çakan, Rough convergence of double sequences, Demonstratio Math. 47(3) (2014), 638–651.
13. 13 E. Dündar, On Rough I2-convergence, Numer. Funct. Anal. Optim. 37(4) (2016), 480–491.
14. 14 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
15. 15 A.R. Freedman, J.J. Sember, Densities and summability, Pacific J. Math. 95 (1981) 293–305.
16. 16 J.A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 4 (1993) 1187–1192.
17. 17 J.A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125(12) (1997) 3625–3631.
18. 18 S. Gähler, 2-metrische Räume und ihre topologische struktur, Math. Nachr. 26 (1963), 115–148.
19. 19 S. Gähler, 2-normed spaces, Math. Nachr. 28 (1964), 1–43.
20. 20 H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (10) (2001), 631–639.
21. 21 H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math. 27 (3) (2001), 321–329.
22. 22 M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math. 2 (1) (2004), 107–113.
23. 23 M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math. 33 (2009), 257–264.
24. 24 M. Gürdal, I. Açık, On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11(2) (2008), 349–354.
25. 25 M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006), 85–91.
26. 26 M.C. Listan-Garcia, F. Rambla-Barreno, Rough convergence and Chebyshev centers in Banach spaces, Numer. Funct. Anal. Optim. 35 (2014) 432–442.
27. 27 P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Mat. 27 (2015) 141-148
28. 28 M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca 61(6) (2011), 933–940.
29. 29 H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim. 22: (2001), 199–222.
30. 30 H. X. Phu, Rough continuity of linear operators, Numer. Funct. Anal. Optim. 23: (2002), 139–146.
31. 31 H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optim. 24: (2003), 285–301.
32. 32 A. ¸ Sahiner, M. Gürdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11(5) (2007), 1477–1484.
33. 33 S. Sarabadan, S. Talebi, Statistical convergence and ideal convergence of sequences of functions in 2-normed spaces, Int. J. Math. Math. Sci. 2011 (2011), 10 pages. doi:10.1155/2011/517841.
34. 34 E. Sava¸s, M. Gürdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat 30(3) (2016), 557–567.
35. 35 I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
36. 36 A. Sharma, K. Kumar, Statistical convergence in probabilistic 2-normed spaces, Math. Sci. 2(4) (2008), 373–390.
37. 37 B.C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malaysian Math. Soc. 20 (1998) 31–33.
38. 38 S. Yegül, E. Dündar, On Statistical Convergence of Sequences of Functions In 2-Normed Spaces, J. Classical Anal. 10(1) (2017), 49–57.
39. 39 S. Yegül, E. Dündar, Statistical Convergence of Double Sequences of Functions and Some Properties In 2-Normed Spaces, Facta Universitatis Ser. Math. Inform. 33(5) (2018), 705–719.
40. 40 S. Yegül, E. Dündar, I2-Convergence of Double Sequences of Functions In 2-Normed Spaces, Univers. J. Math. Appl. 2(3) (2019), 130–137.