Abstract
Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c_{0}^{I}(hat{F}), c^{I}(hat{F}) and l_{infty }^{I}(hat{F}). In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (mu ,nu ). Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.
Highlights
Introduction and preliminariesLet ω, c, c0, l∞ denote sequence space, convergent, null and bounded sequences respectively, with norm x ∞ = supk∈N |xk|
The idea of difference sequence spaces was defined by Kizmaz as follows: λ( ) = x = ∈ ω : ∈ λ, for λ ∈ {l∞, c, c0}
2 Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces we introduce a new type of sequence spaces whose Ftransform is I-convergent with respect to the intuitionistic norm (μ, ν)
Summary
The idea of difference sequence spaces was defined by Kizmaz as follows: λ( ) = x = (xn) ∈ ω : (xn – xn+1) ∈ λ , for λ ∈ {l∞, c, c0}. Khan et al [13] defined the notion of I-convergent Fibonacci difference sequence spaces as cI0(F ), cI(F ) and l∞I (F ). Definition 1.5 ([15]) A sequence x = (xn) is called I-convergent to ξ ∈ R if, for every > 0, the set {n ∈ N : |xn – ξ | ≥ } ∈ I.
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