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In this paper, we introduce the notion of a generalized difference I-convergent (i.e.Δm-I-convergent) and difference I-Cauchy (i.e.Δm-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I*-convergent (i.e.Δm-I*-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.

The proposed article mainly comprises of ideas and motivations that led to the generalization of the usual or the crisp sets. Moving forward we intend to look into how the definitions were modified to suit the meaning of the existing definitions and establish link between them, that is to say that we, after giving formal definitions of the aforementioned sets and norms on these new sets would draw parallel between them and the usual sets and the norm. We will then study some riveting algebraic properties of the same.

Ideal convergence of sequences in neutrosophic normed spaces is defined by Omer Ki¸si [12]. This ¨ paper defines new sequence spaces using the Zweier matrix and neutrosophic norm. We explore (λ, μ)-Zweier convergence, (λ, μ) ideal convergence of double sequences in neutrosophic norm. We show that a double sequence that is (λ, μ)-Zweier convergent or ideal convergent has a unique limit with respect to neutrosophic norm. Additionally, we prove that (λ, μ)-Zweier ideal convergence is equivalent to (λ, μ)-Zweier ideal Cauchy for a double sequence in neutrosophic normed space. [ABSTRACT FROM AUTHOR]

Samarandache [43] introduced neutrosophoic sets to generalize the theory of fuzzy sets. In this paper we modify the definition of neutrosophic normed space with help of continuous neutrosophic t-representable norm. Then we study the statistical graphical convergence and pointwise convergence of the sequences of setvalued functions defined on modified version of neutrosophic normed space and give some related theorems. We also introduce neutrosophic upper and lower semi continuities of set valued maps to develop the link between these convergences. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the neutrosophic I-convergent difference sequence spaces I(Y) (∆) (f) and I0(Y) (∆) (f) defined by modulus function. Also, we define an open ball B(x,€, γ)(f) in neutrosophic norm space (△) defined by modulus function. Furthermore, We construct new topological spaces and look into various topological aspects in neutrosophic I-convergent difference sequence spaces I(Y) (∆) (f) and 10(Y) (∆)(f) defined by modulus function. [ABSTRACT FROM AUTHOR]

The Nörlund matrix Nt in the theory of sequence space was firstly used by Wang. In this paper, by using the Nörlund mean Nt and the notion of ideal convergence, we introduce some new sequence spaces cI 0(Nt), cI (Nt), and lI∞(Nt) as a domain of Nörlund mean. We study some topological and algebraic properties on these spaces. Further, some inclusion concerning these spaces are discussed.

In this paper, we study and introduce a new type of convergence, namely (λ,μ)- Zweier convergence and (λ,μ)- Zweier ideal convergence of double sequences x = (xij) in intuitionistic fuzzy normed space (IFNS), where λ = (λn) and μ= (μm) are two non-decreasing sequences of positive real numbers such that each tending to infinity. Furthermore, we studied (λ,μ)- Zweier Cauchy and (λ,μ)- Zweier ideal Cauchy sequences on the said space and established a relation between them.

Catalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc. Recently ˙Ilkhan formulated the matrix associated with Catalan numbers and studied its domain in c0(C~) and c(C~). In this paper, by employing Catalan matrix defined by Catalan sequence and convergence via ideal, we establish Catalan sequence spaces c I 0 (C~), c I (C~) and ℓ I ∞(C~), study the properties of these corresponding spaces and establish inclusion relations. [ABSTRACT FROM AUTHOR]

In this paper, by using the triangle Hilbert matrix 𝐻 and the notion of ideal convergence for the sequences in intuitionistic fuzzy normed spaces, we introduce some new intuitionistic fuzzy normed sequence spaces as a domain of Hilbert matrix 𝐻, that is, 𝑐❑0(𝜇,𝜈) 𝐼 (𝐻) and 𝑐❑(𝜇,𝜈) 𝐼 (𝐻) Here, 𝑐❑0(𝜇,𝜈) 𝐼 (𝐻) denotes the Hilbert ideal null convergent sequence space with respect to the intuitionistic fuzzy norm and 𝑐❑(𝜇,𝜈) 𝐼 (𝐻) denotes the Hilbert ideal convergent sequence space with respect to the intuitionistic fuzzy norm We also define an open ball with respect to defined sequence space and prove that these open balls are the open sets of these spaces Further, we study some of its topological and algebraic properties We prove that these sequence spaces are linear spaces of In addition, we define a topology with respect to these sequence spaces and obtain that the defined topology is first countable and these topological sequence spaces are Hausdorff spaces We also obtain if and only if results that give an idea about when a sequence belonging to these spaces is classical convergent with respect to the intuitionistic fuzzy norm and when a sequence belonging to these spaces is ideal convergent with respect to the intuitionistic fuzzy norm [ABSTRACT FROM AUTHOR]