In this paper we introduce and study the concepts of almost convergence and almost Cauchy for triple sequences.We show that the set of almost convergent triple sequences of 0's and 1's is of the first category and also almost every triple sequence of 0's and 1's is not almost convergent.

In this paper we define some new sequence spaces and give some topological properties of the sequence spaces s, p) and investigate some inclusion relations.

ABSTRACT. In this paper we introduce a new type of difference operator ∆ n m for fixed m, n ∈ N . We define the sequence spaces ∞ (∆ n m ), c(∆ n m ) and c 0 (∆ n m ) and study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces. These notions generalize many earlier existing notions on difference sequence spaces.

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the statistical convergence of sequence of Bernstein polynomials. In this paper, we introduce the concepts of statistical convergence of Bernstein polynomials and V B −summability and related theorems. We also study Korovkin type-convergence of Bernstein polynomials.

In this paper we introduce the concepts of double lacunary strongly convergence and double lacunary statistical convergence of double interval numbers. We prove some inclusion relations and study some of their properties.

In this paper, we introduce a new generalization of the Hermite polynomials via (p; q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p; q)analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p; q)hyperbolic representations of the (p; q)-Bernstein polynomials. In addition, we obtain a correlation between (p; q)-Hermite polynomials and (p; q)-Bernstein polynomials.

The idea of λ-statistical convergence of single sequences was studied by Alotaibi [39] and double sequences was studied by Savas and Mohiuddine [3] in probabilistic normed spaces. The purpose of this paper is to study statistical convergence of triple sequences in probabilistic normed spaces and give some important theorems.

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