Rough statistical convergence on triple sequences

Abstract

In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of rough statistical cluster points and the set of rough statistical limit points of a triple sequence.

Rough Statistical Convergence in Neutrosophic Normed Spaces

“…In this case, it is denote with 𝑠𝑠𝑠𝑠 − lim 𝑚𝑚,𝑛𝑛,𝑚𝑚→∞ 𝑦𝑦 𝑚𝑚𝑛𝑛𝑚𝑚 = 𝑦𝑦. Now, the definition of rough convergence in the sense of Pringsheim defined using triple sequences by (Debnath and Subramanian, 2017). will be given as:…”

“…Now with the motivation of the studies done in e.g. (Antal et all, 2021), (Debnath and Subramanian, 2017) and (Kisi and Gurdal, 2022) it is possible to move on to the section where new definitions and theorems will be given.…”

“…The rough statistical convergence is defined using triple sequences in (Debnath and Subramanian, 2017). (Antal et all, 2021) studied rough statistical convergence in IFNS and gave main properties this convergence.…”

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 intuitionistic fuzzy normed spaces

“…This idea of rough convergence has motivated many authors to use this concept not only in usual sense but also in statistical mode in the different forms like double sequences [17,18] and triple sequences [7], lacunary sequences [13], real valued function sequences [16], ideals [19,26] etc. Besides these above mentioned forms it is also established for the different spaces like metric spaces [6], random normed spaces [1], cone metric spaces [4], probabilistic normed spaces [29] etc.…”