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In this paper, our aim is to make a novel interpretation of relation between (N̅,p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (N̅,p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (Pm) and Qn are Tauberian conditions for (N̅,p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N̅,p,q) summability method for fuzzy positive linear operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of summability methods that can be applied to lacunary double statistical convergence in topological groups and we also prove some theorems. [ABSTRACT FROM AUTHOR]

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 concept of statistical convergence is one of the most active area of research in the field of summability. Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory. In this paper, we introduce the idea of double Jλ -statistical convergence in a locally solid Riesz space and study some of its properties by using the mathematical tools of the theory of topological vector spaces. [ABSTRACT FROM AUTHOR]

In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "lim" with arbitrary linear regular summability methods G we consider the notion of a generalized continuity ((G1,G2)-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces. [ABSTRACT FROM AUTHOR]

Abstract: Following the line of recent works of Das et al. (2011)  and Savas and Das (2011)  we apply the notion of ideals to strong matrix summability, and in this note, we introduce the notion of strong -summability with respect to an Orlicz function. We make certain investigations on the classes of sequences arising out of this new summability method. [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]