• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.268-271
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• 2008

In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.613-620
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• 2021

In this paper, we introduce the definition of weakly convergent sequence in fuzzy normed spaces. We investigate relationship between convergent sequence and weakly convergent sequence in fuzzy normed spaces. We also study the dual spaces of a standard fuzzy normed space and 01-fuzzy normed space.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.185-199
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• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.541-552
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• 2023

In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.391-399
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• 2010

In this paper, we introduce the notions of the fuzzy statistical convergence of sequences, the fuzzy statistical Cauchy sequence on a fuzzy normed linear space. And we investigate some properties of the related completeness.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.347-354
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• 2008

In this paper, we will show that ($CF(X,K),{\chi}_{{\parallel}{\mid}{\cdot}{\parallel}{\mid}}$) is a fuzzy Banach space using that the dual space $X^*$ of a normed linear space X is a crisp Banach space. And for a normed linear space Y instead of a scalar field K, we obtain ($CF(X,Y),{\rho}^*$) is a fuzzy Banach space under the some conditions.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.541-555
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• 2009

The primary purpose of this paper is to prove the fuzzy version of Riesz theorem in n-normed linear space as a generalization of linear n-normed space. Also we study some properties of fuzzy n-norm and introduce a concept of fuzzy anti n-norm.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.9-15
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• 1997

The main goal of this paper is to investigate some properties of a quotient fuzzy seminorm ${\rho}_q$ induced by a fuzzy seminorm ${\rho}={\chi}_{B_{{\parallel}{\cdot}{\parallel}}}$ on a normed linear space X.