• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.475-480
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• 1998

We show that the foundational isomorphism exists in the category of filter convergence spaces which contains the category of Banach spaces as a replete subcategory.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.47-69
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• 2006

In this paper, an idea of graded fuzzy net is introduced; its convergence is studied; Relations between g-net and g-filter are established in L-fuzzy setting.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.105-124
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• 2005

In this paper convergence of fuzzy filters and graded fuzzy filters have been studied in graded L-fuzzy topological spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.59-64
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• 2009

In this paper, we study the relations between L-fuzzy topologies and L-filters on a strictly two-sided, commutative quantale lattice L. We define an L-fuzzy neighborhood filter and introduce the notion of L-filter convergence in L-fuzzy topological spaces.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.813-826
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• 2009

In this paper, we generalize the notions of preserving and strongly preserving maps to arbitrary set based topological categories. Further, we obtain characterizations of each of these concepts as well as interprete analogues and generalizations of theorems of Gerlits at al [20] in the categories of filter and local filter convergence spaces.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.331-341
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• 2014

In this article we introduce the sequence spaces $_2c^I_0(f,p)$, $_2c^I(f,p)$ and $_2l^I_{\infty}(f,p)$ for a modulus function f, where $p=(p_k)$ is a sequence of positive reals and study some of the properties of these spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.6
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• pp.781-785
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• 2011

The notions of soft filters, ultra soft filters and bases of a soft filter are introduced and their basic properties are investigated. The adherence and convergence of soft filters in soft topological spaces with related results is also discussed.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.901-911
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• 2023

In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.547-559
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• 2021

We first define the notions of filter continuous, filter sequentially continuous and filter strongly continuous in the framework of fuzzy normed space (FNS), and then we introduce the notion of filter slowly oscillating sequences in the setting of FNS and shows that this notion is stronger than slowly oscillating sequences. Further, we define the concept of filter slowly oscillating continuous functions, filter Cesàro slowly oscillating sequences as well as some other related notions in the aforementioned space and investigate several related results.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.