Rough $I$-statistical convergence of double sequences in normed linear spaces
Downloads
DOI:
https://doi.org/10.26637/MJM0701/0011Abstract
The notion of I -statistical convergence of a double sequence was first introduced by Belen et. al.[ 2 ] and the notion of rough convergence of a sequence was first introduced by Phu [ 19 ]. In this paper we introduce and study the notion of rough I -statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I -statistical limit set of a double sequence and discuss about some topological properties of this set.
Keywords:
Double sequence, I -statistical convergence, rough I -statistical convergence, I - statistical boundedness, rough I -statistical limit setMathematics Subject Classification:
Mathematics- Pages: 55-61
- Date Published: 01-01-2019
- Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)
S. Aytar, Rough statistical covergence, Numer. Funct. Anal. And Optimiz., 29(3)(2008), 291-303.
C. Belen and M. Yildirim, On generalized statistical convergence of double sequences via ideals, Ann. Univ. Ferrara 58(1) (2012), 11-20.
P. Das and P. Malik., On the statistical and I-variation of double sequences, Real Anal. Exchange, 33(2007), 351-364.
P. Das, P. Kostyrko, W. Wilczyński and P. Malik., I and $I^*$-convergence of double sequences, Math. Slovaca, $58(2008), 605-620$.
P. Das and P. Malik., On extremal I-limit points of double sequences, Tatra Mt. Math. Publ, 40 (2008), 91-102.
K. Demirci., I-limit superior and limit inferior, Math. Commun., 6(2)(2001), 165-172.
K. Dems., On I-Cauchy sequences, Real Anal. Exchange, 30(1)(2004/2005), 123-128.
E. Dündar., On rough $I_2$-convergence of double sequences, Numer. Funct. Anal.And Optimiz., DOI:10.1080/01630563.2015.1136326.
P. Kostyrko, T. Šalát and W. Wilczyński., I-convergence, Real Anal. Exchange, 26(2)(2000/2001), 669-685.
P. Kostyrko, M. Macaz, T. Šalát and M. Sleziak., Iconvergence and external I-limit points, Math. Slovaca, 55(4)(2005), 443-454.
B.K. Lahiri and P. Das., I and $I^*$ convergence in topological spaces, Math. Bohemica, 130(2)(2005), 153-160.
P. Malik and M. Maity., On rough convergence of double sequence in normed linear spaces, Bull. Allah. Math. Soc., 28(1)(2013), 89-99.
P. Malik and M. Maity., On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat., (2016) 27: 141-148.
P. Malik, M. Maity and A. Ghosh, A note on rough I-convergence of double sequences. arxiV preprint arXiv.,(2016) 1603.01363.
P. Malik and A. Ghosh.,On I-statistical Cluster point of double sequences. arxiv preprint arxiV.,(2017) 1703.07177.
Moricz, F., Statistical convergence of multiple sequences, Arch. Math. 81, 82-89, 2003.
M. Mursaleen and O.H.H. Edely., Statistical Convergence of double sequences, J. Math. Anal. Appl, 288 (2003), 223-231.
S.K. Pal, D. Chandra and S. Dutta., Rough ideal convergence, Hacettepe J. of Math. and Stat., 42(6)(2013),
H.X. Phu., Rough convergence in normed linear spaces, Numer. Funct. Anal. And Optimiz., 22(2001), 201-224.
H.X. Phu., Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. And Optimiz., 24(2003), 285-301.
A. Pringsheim., Zur theortie der Gamma-Functionen, Math. Annalen., 31 (1888), 455-481.
B. Tripathy and B. C. Tripathy., On I-convergent double sequences, Soochow Journal of Mathematics., 31(4)(2005), 549-460.
B. C. Tripathy., Statistically convergent double sequences, Tamkang journal of mathematics., 34(3)(2003), 231-237.
U. Yamanci, and M. Gürdal., $mathscr{I}$-statistically pre-Cauchy double sequences, Global Journal of Mathematical Analysis, 2 (4) (2014), 297-303.
A. Zygmund., Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
- NA
Similar Articles
- Soumia Saidi, Mustapha Fateh Yarou, On viscosity solution of Hamilton-Jacobi-Belman equations , Malaya Journal of Matematik: Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
