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.

Rough Statistical Convergence of Double Sequences in Probabilistic Normed Spaces

“…Malik and Maity [23,24] has defined rough convergence and rough statistical convergence of double sequences in normed linear spaces. After that, the research work on this concept is still being carried out in different directions by Antal et al [4], Ghosal and Banerjee [13], Hossain and Banerjee [14], Kişi and Ünal [18], Özcan and Or [26] and references cited therein.…”

Rough Statistical Convergence in L-Fuzzy Normed Spaces

“…On the other hand, Antal et al [17] studied the notion of rough statistical convergence in intuitionistic fuzzy normed spaces, Antal et al [18] in probabilistic normed spaces, and S. Debnath, D. Rakshit [19] in metric spaces. In addition to the above studies in different spaces, Özcan and Aykut [20] performed double sequences, S. Debnath and N. Subramanian [21] performed triple sequences, and Ö. Kis . i and E. Dündar [22] examined the concept in question for the Lacunary sequences.…”

Rough Statistical Convergence in L-Fuzzy Normed Spaces

“…On the other hand, Antal et al [17] studied the notion of rough statistical convergence in intuitionistic fuzzy normed spaces, Antal et al [18] in probabilistic normed spaces, and S. Debnath, D. Rakshit [19] in metric spaces. In addition to the above studies in different spaces, Özcan and Or [20] performed double sequences, S. Debnath and N. Subramanian [21] performed triple sequences, and Ö. Kisi and E. Dündar [22] examined the concept in question for the Lacunary sequences. In this article, we provide some results regarding the rough statistical convergence of sequences on ℒ −fuzzy normed spaces and study the relations between rough convergent, rough statistical convergent, and rough statistical bounded sequences.…”