Some Properties of Rough Statistical Convergence in 2-Normed Spaces

Year 2020, Volume: 3 Issue: 1, 145 - 149, 15.12.2020

Mukaddes Arslan Erdinç Dündar

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 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 M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math. 42 (2018), 491–502.
• 3 M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl. 10(3) (2018), 1–9.
• 4 M. Arslan, E. Dündar, On Rough Convergence in 2-Normed Spaces and Some Properties, Filomat 33(16) (2019), 5077–5086.
• 5 M. Arslan, E. Dündar, Rough Statistical Convergence in 2-Normed Spaces, J. Appl. Math. Inform. (in review).
• 6 S. Aytar, Rough statistical convergence,Numer. Funct. Anal. Optim. 29(3-4): (2008), 291–303.
• 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 S. Aytar, Rough statistical cluster points, Filomat 31(16): (2017), 5295–5304.
• 9 H. Çakallı and S. Ersan, New types of continuity in 2-normed spaces, Filomat 30(3) (2016), 525–532.
• 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 E. Dündar, C. Çakan, Rough I-convergence, Gulf J. Math. 2(1) (2014), 45–51.
• 12 E. Dündar, C. Çakan, Rough convergence of double sequences, Demonstratio Math. 47(3) (2014), 638–651.
• 13 E. Dündar, On Rough I2-convergence, Numer. Funct. Anal. Optim. 37(4) (2016), 480–491.
• 14 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
• 15 A.R. Freedman, J.J. Sember, Densities and summability, Pacific J. Math. 95 (1981) 293–305.
• 16 J.A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 4 (1993) 1187–1192.
• 17 J.A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125(12) (1997) 3625–3631.
• 18 S. Gähler, 2-metrische Räume und ihre topologische struktur, Math. Nachr. 26 (1963), 115–148.
• 19 S. Gähler, 2-normed spaces, Math. Nachr. 28 (1964), 1–43.
• 20 H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (10) (2001), 631–639.
• 21 H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math. 27 (3) (2001), 321–329.
• 22 M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math. 2 (1) (2004), 107–113.
• 23 M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math. 33 (2009), 257–264.
• 24 M. Gürdal, I. Açık, On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11(2) (2008), 349–354.
• 25 M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006), 85–91.
• 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 P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Mat. 27 (2015) 141-148
• 28 M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca 61(6) (2011), 933–940.
• 29 H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim. 22: (2001), 199–222.
• 30 H. X. Phu, Rough continuity of linear operators, Numer. Funct. Anal. Optim. 23: (2002), 139–146.
• 31 H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optim. 24: (2003), 285–301.
• 32 A. ¸ Sahiner, M. Gürdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11(5) (2007), 1477–1484.
• 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 E. Sava¸s, M. Gürdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat 30(3) (2016), 557–567.
• 35 I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
• 36 A. Sharma, K. Kumar, Statistical convergence in probabilistic 2-normed spaces, Math. Sci. 2(4) (2008), 373–390.
• 37 B.C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malaysian Math. Soc. 20 (1998) 31–33.
• 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 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 S. Yegül, E. Dündar, I2-Convergence of Double Sequences of Functions In 2-Normed Spaces, Univers. J. Math. Appl. 2(3) (2019), 130–137.