Article

# Fuzzy real valued lacunary I-convergent sequences

(Impact Factor: 1.34). 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.

### Full-text

Available from: Bipan Hazarika, Oct 28, 2014
• Source
• "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 "
##### Article: Ideal convergent sequence spaces over p-metric spaces defined by Musielak-modulus functions
[Hide abstract]
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
• Source
• "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. "
##### Article: Lacunary ideal convergence in probabilistic normed spaces
[Hide abstract]
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.
• Source
• "The existing literature on ideal convergence and its generalizations appears to have been restricted to real or complex sequences, but in recent years these ideas have been also extended to the sequences in fuzzy normed [11] and intuitionistic fuzzy normed spaces [7, 10, 12, 15–17]. Further details on ideal convergence can be found in [6] [13] [20] [27] and many others. Now we recall some notations and basic definitions that we are going to use in this paper. "
##### Article: On λ-ideal convergent interval valued difference classes defined by Musielak–Orlicz function
[Hide abstract]
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. In this paper, using λ-ideal convergence as a variant of the notion of ideal convergence, the difference operator Δn and Musielak–Orlicz functions, we introduce and examine some generalized difference sequences of interval numbers, where λ=(λ m ) is a nondecreasing sequence of positive real numbers such that λ m+1≤λ m +1,λ 1=1,λ m →∞(m→∞). We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.
Acta Mathematica Vietnamica 12/2013; 38(4). DOI:10.1007/s40306-013-0041-0