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Fuzzy real valued lacunary I-convergent sequences

Applied Mathematics Letters (Impact Factor: 1.48). 03/2012; 25(3):466-470. DOI: 10.1016/j.aml.2011.09.037
Source: DBLP

ABSTRACT In this article, we introduce the concept of lacunary II-convergent sequence of fuzzy real numbers and study some basic properties.

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Available from: Bipan Hazarika, Oct 28, 2014
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    • "The notion of lacunary ideal convergence of real sequences was introduced in [17] [18]. Hazarika [19] [20] [21] introduced the lacunary ideal convergent sequences of fuzzy real numbers and studied some basic properties of this notion. Hazarika [22] introduced the notion of lacunary ideal convergent double sequences of fuzzy real numbers. "
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    ABSTRACT: An ideal I is a family of subsets of which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic.
    02/2015; 2. DOI:10.1016/j.joems.2014.07.002
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    • "The notion of deal convergence was introduced first by Kostyrko et al. [24] as a generalization of statistical convergence which was further studied in toplogical spaces by Kumar et al. [25] [26] and also more applications of ideals can be deals with various authors by B.Hazarika [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] and B.C.Tripathy and B. Hazarika [40] [41] [42] [43]. A family I & 2 Y of subsets of a non-empty set Y is said to be an ideal in Y if "
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    ABSTRACT: In this paper we introduce the I- of χ2χ2 sequence spaces over p-metric spaces defined by Musielak function. We also examine some topological properties and prove some inclusion relation between these spaces.
    10/2014; 22(3). DOI:10.1016/j.joems.2013.12.016
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    • "Further details on ideal convergence can be found in ([6] [14] [15] [16] [26] [28] [29] [30] [31] [32] [39] [50] [55] [57] [58]), and many others. The notion of lacunary ideal convergence of real sequences was introduced in ([9] [56]) and Hazarika ([24] [25]), was introduced the lacunary ideal convergent sequences of fuzzy real numbers and studied some properties. Debnath [13] introduced the notion lacunary ideal convergence in May 13, 2014. "
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    ABSTRACT: An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_k)$ of real numbers is said to be lacunary $I$-convergent to a real number $\ell$, if for each $ \varepsilon> 0$ the set $$\left\{r\in \mathbb{N}:\frac{1}{h_r}\sum_{k\in J_r} |x_{k}-\ell|\geq \varepsilon\right\}$$ belongs to $I.$ The aim of this paper is to study the notion of lacunary $I$-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary $I$-limit points and lacunary $I$-cluster points have been defined and the relation between them has been established. Furthermore, lacunary-Cauchy and lacunary $I$-Cauchy sequences are introduced and studied. Finally, we provided example which shows that our method of convergence in probabilistic normed spaces is more general.
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