Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces
Abstract
This paper proposes rough convergence and rough statistical convergence of a double sequence in intuitionistic fuzzy normed spaces. It then defines the rough statistical limit points and rough statistical cluster points of a double sequence in these spaces. Afterwards, this paper examines some of their basic properties. Finally, it discusses the need for further research.
Keywords
Rough convergence, Statistical convergence, Rough statistical convergence, Intuitionistic fuzzy normed spaces
References
- H. Fast, Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), (1951) 241-244.
- H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicae, 2, (1951) 73-74.
- A. Zygmund, Trigonometricheskii ryady, Moscow, Leningrad, Gostekhizdat, 1939.
- M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, Journal of Mathematical Analysis and Applications, 288(1), (2003) 223-231.
- H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis and Optimization, 22(1-2), (2001) 199-222.
- S. Aytar, Rough statistical convergence, Numerical Functional Analysis and Optimization, 29(3-4), (2008) 291-303.
- P. Malik, M. Maity, On rough convergence of double sequence in normed linear spaces, Bulletin of Theallahabad Mathematical Society, 28(1), (2013) 89-99.
- P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Matematika, 27(1-2), (2016) 141-148.
- U. Yamancı, M. Gürdal, I-statistically pre-cauchy double sequences, Global Journal of Mathematical Analysis, 2(4), (2014) 297-303.
- Ö. Kişi, E. Dündar, Rough ${I}_{2}$-lacunary statistical convergence of double sequences, Journal of Inequalities and Applications, 2018, Article No: 230, (2018) 1-16.