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We introduce a convergence of weight g : N→[0,∞) where g(n)→∞ and n=g(n)↛0 with respect to a summability matrix method A for sequences (which generalizes the notion of A-convergence of order α; 0 < α ≤ 1 [BOCCUTO, A.-DAS, P.: On matrix methods of convergence of order (α) in (ℓ)-groups, Filomat 29 (2015), 2069-2077] in a (ℓ)-group. We prove some basic results including a Cauchy-type criterion. Finally a closedness result for the space of such convergent sequences is proved. [ABSTRACT FROM AUTHOR]

The goal of this article is to present multidimensional matrix characterization of geometrically dominated double sequences. We begin this characterization with the following definition of geometrically dominated factorable double sequence space. LetG″ denote a family of double complex number sequences that are dominated by a P-convergence geometric factorable double sequence, that is, This definition will be use to present the theorems similar to the following. The four-dimensional matrix is anG″ − l″ if and only ifand Other implication will also be presented. [ABSTRACT FROM AUTHOR]

In this paper we introduce some new double sequence spaces of fuzzy real numbers by combining I-convergence, Orlicz function and four dimensional matrix and we examine some properties of the resulting sequences spaces of fuzzy numbers. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a series of four-dimensional matrix characterizations of statistically asymptotically equivalent double and single sequences. These characterizations begins with the presentation of definitions for asymptotically equivalent and asymptotically statistical equivalent of multiple L for double and single sequences. The type of questions we provided answers for are those of the following sort. What are the necessary and sufficient conditions on the entries A that ensure the preservation of statistically asymptotically equivalent rate of convergence. [Copyright &y& Elsevier]

This paper presents multidimensional characterizations of equivalence classes of double sequences. These characterizations will be analyzed by presenting theorems of the following type: If A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \;{\rm equivalent \; to}\; b\}}$$ then there exists a $${b^{\prime} \in S^{\prime\prime}_{0}}$$ such that b converges faster than b′ and A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \; {\rm equivalent \; to}\; b^{\prime}\}.}$$ [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce certain new sequence spaces of fuzzy numbers defined by -convergence using sequences of Orlicz functions and a difference operator of order . We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to present the following multidimensional category theorem for double sequences via four-dimensional matrix transformations. The set of second category double subsequences of the double sequence is summable by a four-dimensional RH-regular matrix if and only if is -convergent. This theorem is established using multidimensional sliding hump constructions for bounded and unbounded doubles sequences. [Copyright &y& Elsevier]

Abstract: In this paper, following the line of Savas and Das (2011) , we provide a new approach to two well-known summability methods by using ideals, introduce new notions, namely, -statistical convergence and -lacunary statistical convergence, investigate their relationship, and make some observations about these classes. [Copyright &y& Elsevier]

Abstract: In this paper we make a new approach to the notions of -summability and -statistical convergence by using ideals and introduce new notions, namely, -summability and -statistical convergence. We mainly examine the relation between these two new methods as also the relation between -statistical convergence and -statistical convergence introduced by the authors recently. We carry out the whole investigation in normed linear spaces. [Copyright &y& Elsevier]

In this paper we introduce some new double sequence spaces of fuzzy numbers using Orlicz function and also we examine that if a sequence of fuzzy numbers is double strongly convergent with respect to an Orlicz function then it is double statistical convergent. [ABSTRACT FROM AUTHOR]

In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces. [ABSTRACT FROM AUTHOR]