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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 have extended the concepts of I-statistical limit superior and I-statistical limit inferior to I-statistical φ-limit superior and I-statistical φ-limit inferior and studied some of their properties for sequence of real numbers. [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]

The goal of this paper is to study some new sequence spaces of order α that are defined using modulus function and infinite matrix A. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and examine some properties of A-statistical convergence of order α by using φ - function, modulus function and generalized three parametric real matrix A. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce the concept of λ-statistical convergence of weight g of fuzzy numbers by using ideal. In addition to this concept, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

In this paper by using the Iacunary sequence and Orlicz function ɸ, we introduce a new concept of Iacunary statistically ɸ-convergence, as a generalization of the statistically ɸ--convergence and ɸ--convergence. Based on this concepts, introduce a new sequence space Se -- ɸ and investigate some of its basic properties. Also studied some inclusion relations. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [6] (where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : N → [0;∞) is a function satisfying g (n) → ∞ and n/g (n) → 0. We mainly investigate their relationship and also make some observations about these classes. Our results extend the recent results of [7]. [ABSTRACT FROM AUTHOR]

We introduce rough I-statistical convergence as an extension of rough convergence. We define the set of rough I-statistical limit points of a sequence and analyze the results with proofs. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence problems of fixed points for multi-valued mappings and minimization theorems in fuzzy metric spaces. [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]

In this article, we study approximation properties of single hidden layer neural networks with weights varying in finitely many directions and with thresholds from an open interval. We obtain a necessary and simultaneously sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons. [ABSTRACT FROM PUBLISHER]

In this paper, using the difference operator of order m and a lacunary sequence $$\theta = (k_{r})$$ , we introduce and examine some classes of sequences of fuzzy numbers. Furthermore, we study some of their properties like completeness, solidity, symmetricity and convergence free. We also give some inclusion relations related to these classes. [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]

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 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]

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]

In this paper, using the difference operator of order m, the sequences of Orlicz functions and double lacunary sequence we introduce and study some classes of sequences of fuzzy numbers defined by I-convergence. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these 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 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]

Abstract: In this work, we generalize the lacunary almost bounded variation sequence spaces to lacunary almost -bounded variation sequence spaces. Also some topological results and inclusion relations of such spaces have been discussed. [Copyright &y& Elsevier]

Abstract: In this paper, we determine sufficient condition for the transpose of an E–J generalized Hausdorff matrix to be of type . [ABSTRACT FROM AUTHOR]

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]

The article generalizes the notion of orthogonal fuzzy metric space into a broader term, named as orthogonal picture fuzzy metric space. The obtained results improve and extend the idea of the orthogonal fuzzy metric space and its related results. However, this article outstretches the above-mentioned notion further into a newly defined concept, named as orthogonal picture fuzzy metric space. A detailed insight is given into the topic by presenting some fixed point results in the frame of the newly defined structure. To elaborate the results more precisely, some concrete examples are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider some F-contraction mappings in a dualistic partial metric space and to provide sufficient related conditions for the existence of a fixed point. The obtained results are extensions of several ones existing in the literature. Moreover, we present examples and an application to support our results. [ABSTRACT FROM AUTHOR]