Ideal convergence in 2-fuzzy 2-normed spaces

Rashid, M. H. M.; v{c}inac, Ljubi v{s}a D.R. Ko

doi:10.15672/hjms.2016.406

Cited by 10 publications

(4 citation statements)

References 31 publications

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“…Arslan and Dündar [8] also explored I-convergence, I-convergence, I-Cauchy, and I * -Cauchy sequences of functions within 2-normed spaces. It is important to emphasize that significant progress in this field has been well-documented in references [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Altaweel et al [18] adapted this theory to the fuzzy metric space, while Kočinac and Rashid [9] expanded it to encompass the probabilistic metric space. Furthermore, Rashid and Kočinac and Rashid [10] delved into the investigation of the ideal of convergence within the framework of fuzzy 2-normed space. The introduction of I * -convergence in [17] spurred extensive research efforts aimed at uncovering its relationship with I-convergence.…”

Section: Introductionmentioning

confidence: 99%

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Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Bani-Ahmad,

Rashid

2023

Symmetry

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In our ongoing study, we explore the concepts of I3-Cauchy and I3-Cauchy for triple sequences in the context of random 2-normed spaces (RTNS). Moreover, we introduce and analyze the notions of I3-convergence, I3-convergence, I3-limit points, and I3-cluster points for random 2-normed triple sequences. Significantly, we establish a notable finding that elucidates the connection between I3-convergence and I3-convergence within the framework of random 2-normed spaces, highlighting their interrelation. Additionally, we provide an illuminating example that demonstrates how I3-convergence in a random 2-normed space might not necessarily imply I3-convergence. Our observations underscore the importance of condition (AP3) when examining summability using ideals. Furthermore, we thoroughly investigate the relationship between the properties (AP) and (AP3), illustrating through an example how the latter represents a less strict condition compared to the former.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Bani-Ahmad,

Rashid

2023

Symmetry

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“…The concepts of fuzzy norm and α-norm were introduced by Bag and Samanta in [3]. The concept of fuzzy n-normed linear spaces has been studied by many authors like [11,14,17]. In 2012, Park and Alaca [16] introduced the concept of 2-fuzzy n-normed linear space or fuzzy n-normed linear space of the set of all fuzzy sets of a non-empty set.…”

Section: Introductionmentioning

confidence: 99%

On some topological properties of intuitionistic $2$-fuzzy $n$-normed linear spaces

Kočinac

Khan

Alshlool

et al. 2020

Hacettepe Journal of Mathematics and Statistics

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Motivated by the notion of n-norm due to Gähler, in this article we define the concept of intuitionistic 2-fuzzy n-normed space in general setting of t-norm as a generalization of intuitionistic fuzzy normed space in the sense of Bag and Samanta. Further we define the notion of α-n-norm corresponding to intuitionistic 2-fuzzy n-norm. In addition, we discuss some basic properties of convergence and completeness for intuitionistic 2-fuzzy n-normed spaces.

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“…Recently, the notion of statistical convergence of double sequences has been defined and studied by Mursaleen and Edely [25]; and for fuzzy numbers by Savaş and Mursaleen [32]. The notion of ideal convergence of double sequences in the topology induced by fuzzy 2-norm has been studied by Kočinac and Rashid [30], in 2-fuzzy 2-norm spaces by Rashid and Kočinac [20]. Quite recently, Das et al [5] studied the notion of I and I *convergence of double sequences in R.…”

Section: Introductionmentioning

confidence: 99%