Statistical convergence on intuitionistic fuzzy normed spaces

Karakuş, Sevda; Demirci, Kami̇l; Duman, Oktay

doi:10.1016/j.chaos.2006.05.046

Cited by 90 publications

(57 citation statements)

References 26 publications

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“…Then f is an admissible ideal in , and -statistical convergence coincides with the notion of statistical convergence introduced in Ref. 22.…”

Section: -λ-Statistical Convergence On Ifnsmentioning

confidence: 71%

A generalized statistical convergence in intuitionistic fuzzy normed spaces

Savaş¹,

Gürdal²

2015

ScienceAsia

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ABSTRACT:In this paper, we introduce the notion of -[V, λ]-summability and -λ-statistical convergence with respect to the intuitionistic fuzzy norm (µ, v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between -λ-statistical convergence and -statistical convergence in the corresponding intuitionistic fuzzy normed space.

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“…Then f is an admissible ideal in , and -statistical convergence coincides with the notion of statistical convergence introduced in Ref. 22.…”

Section: -λ-Statistical Convergence On Ifnsmentioning

confidence: 71%

A generalized statistical convergence in intuitionistic fuzzy normed spaces

Savaş¹,

Gürdal²

2015

ScienceAsia

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“…The ideal convergence provides a general framework to study the properties of various types of convergence. Additionally, Karakuş et al [13] defined statistical convergence in intuitionistic fuzzy normed spaces (IFNS for short) and Mursaleen et al [22] investigated statistical convergence of double sequences in IFNS. Quite recently, in [10], Karakaya et al defined and studied statistical convergence of sequences of functions in IFNS.…”

Section: Introductionmentioning

confidence: 99%

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

Karakaya¹,

Şi̇mşek²,

Ertürk³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed space.

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“…Recently, statistical convergence and some of its related concepts for fuzzy numbers have been studied in [7][8][9]. Quite recently, the idea of statistical convergence in intuitionistic fuzzy normed spaces for single sequences has been studied in [10,11]; and for double sequences by Mursaleen and Mohiuddine [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, {x} K is a nonthin subsequence of x if K does not have density zero. Definition 1.9 [10,12]. Let (X, μ, ν, *, ◊) be an intuitionistic fuzzy normed space.…”

Section: Introductionmentioning

confidence: 99%